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Journal articles on the topic 'Von Neumann stability condition'

Author: Grafiati

Published: 25 January 2025

Last updated: 31 July 2025

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1

Kamel, Aladin H. "A stability checking procedure for finite-difference schemes with boundary conditions in acoustic media." Bulletin of the Seismological Society of America 79, no. 5 (1989): 1601–6. http://dx.doi.org/10.1785/bssa0790051601.

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Abstract The manner in which boundary conditions are approximated and introduced into finite-difference schemes has an important influence on the stability and accuracy of the results. The standard von Neumann stability condition applies only for points which are not in the vicinity of the boundaries. This stability condition does not take into consideration the effects caused by introducing the boundary conditions to the scheme. In this paper, we extend the von Neumann condition to include boundary conditions. The method is based on studying the time propagating matrix which governs the space

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2

Li, Yong Heng, and Xia Li. "Extension of Von Neumann Model of National Economic System." Applied Mechanics and Materials 55-57 (May 2011): 101–4. http://dx.doi.org/10.4028/www.scientific.net/amm.55-57.101.

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The Von Neumann Model on national economical system is investigated. A new discrete-time input-output model on national economic system based on the classic Von Neumann Model is provided and the stability of this kind of model is researched. This new system belongs to the singular system. By the new mathematic method, this singular linear system will not be converted into the general linear system. Finally, a sufficient stability condition under which the discrete-time singular Extended Von Neumann Model is admissible is proved.

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3

Haney, Matthew M. "Generalization of von Neumann analysis for a model of two discrete half-spaces: The acoustic case." GEOPHYSICS 72, no. 5 (2007): SM35—SM46. http://dx.doi.org/10.1190/1.2750639.

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Evaluating the performance of finite-difference algorithms typically uses a technique known as von Neumann analysis. For a given algorithm, application of the technique yields both a dispersion relation valid for the discrete time-space grid and a mathematical condition for stability. In practice, a major shortcoming of conventional von Neumann analysis is that it can be applied only to an idealized numerical model — that of an infinite, homogeneous whole space. Experience has shown that numerical instabilities often arise in finite-difference simulations of wave propagation at interfaces with

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4

Wu, Xiu Mei, Tao Zi Si, and Lei Jiang. "Stable Computer Control Algorithm of Von Neumann Model." Advanced Materials Research 634-638 (January 2013): 4026–29. http://dx.doi.org/10.4028/www.scientific.net/amr.634-638.4026.

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The problem of computer control algorithm for the singular Von Neumann input-output model is researched. A kind of new mathematic method is applied to study the singular systems without converting them into general systems. A kind of stability condition under which the singular input-output model is admissible is proved with the form of linear matrix inequality. Based on this, a new state feedback stability criterion is established. Then the formula of a desired state feedback controller is derived.

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5

Jimrise, O. Ochwach, W. Musundi Sammy, and O. Okongo Mark. "Stability Analysis Of The Modified Advection-Dispersion Model For Nitrate Leaching Into Groundwater." Journal of Progressive Research in Mathematics 14, no. 2 (2018): 2334–40. https://doi.org/10.5281/zenodo.3974128.

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Nitrogen is a vital nutrient that enhances plant growth which has motivated the intensive use of nitrogen based fertilizers to boost crop productivity. However, Pollution by nitrate is a globally growing problem due to the population growth, increase in the demand for food and inappropriate Nitrogen application. The complexities and challenges in quantifying nitrate leaching have led to development of a range of measurement and modeling techniques. However, most of them are not widely applied due to their inaccuracy. This calls for new approaches in which nitrate leaching can be analysed in or

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6

WESSELING, P. "von Neumann stability conditions for the convection-diffusion eqation." IMA Journal of Numerical Analysis 16, no. 4 (1996): 583–98. http://dx.doi.org/10.1093/imanum/16.4.583.

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7

Roman, Marcel, and Adrian Sandovici. "On the Equality A=A1A2 for Linear Relations." Axioms 14, no. 4 (2025): 239. https://doi.org/10.3390/axioms14040239.

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Assume that A, A1, and A2 are three selfadjoint linear relations (multi-valued linear operators) in a certain complex Hilbert space. In this study, conditions are presented for the multi-valued operator equality A=A1A2 to hold when the inclusion A⊂A1A2 is assumed to be satisfied. The present study is strongly motivated by the invalidity of a classical result from A. Devinatz, A.E.Nussbaum, and J. von Neumann in the general case of selfadjoint linear relations. Two types of conditions for the aforementioned equality to hold are presented. Firstly, a condition is given in terms of the resolvent

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8

M. Jemimah, M. Alpha, and Abubakar Alkasim. "Exact Solution of Couple Burgers’ Equation using Cubic B-Spline Collocation Method for Fluid Suspension/Colloid under the Influence of Gravity." African Journal of Advances in Science and Technology Research 14, no. 1 (2024): 73–85. http://dx.doi.org/10.62154/ymthy538.

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In this research, Cubic B-Spline plane method was used to solve numerically the one-dimensional Burger’s Equation with initial condition , boundary conditions; . The cubic trigonometric B-spline was used for interpolating the solutions at each time and using the Von-Neumann method to check the stability. The obtained numerical result showed that the method was efficient, robust and reliable for solving Burgers’ Equation accurately even involving high Reynolds numbers for which the exact solutions have failed.

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9

Hafiz, Khandaker Md Eusha Bin, and Laek Sazzad Andallah. "Second Order Scheme For Korteweg-De Vries (KDV) Equation." Journal of Bangladesh Academy of Sciences 43, no. 1 (2019): 85–93. http://dx.doi.org/10.3329/jbas.v43i1.42237.

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The kinematics of the solitary waves is formed by Korteweg-de Vries (KdV) equation. In this paper, a third order general form of the KdV equation with convection and dispersion terms is considered. Explicit finite difference schemes for the numerical solution of the KdV equation is investigated and stability condition for a first-order scheme using convex combination method is determined. Von Neumann stability analysis is performed to determine the stability condition for a second order scheme. The well-known qualitative behavior of the KdV equation is verified and error estimation for compari

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10

Quintana-Murillo, J., and S. B. Yuste. "An Explicit Numerical Method for the Fractional Cable Equation." International Journal of Differential Equations 2011 (2011): 1–12. http://dx.doi.org/10.1155/2011/231920.

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An explicit numerical method to solve a fractional cable equation which involves two temporal Riemann-Liouville derivatives is studied. The numerical difference scheme is obtained by approximating the first-order derivative by a forward difference formula, the Riemann-Liouville derivatives by the Grünwald-Letnikov formula, and the spatial derivative by a three-point centered formula. The accuracy, stability, and convergence of the method are considered. The stability analysis is carried out by means of a kind of von Neumann method adapted to fractional equations. The convergence analysis is ac

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11

Luiz, Kariston Stevan, Juniormar Organista, Eliandro Rodrigues Cirilo, Neyva Maria Lopes Romeiro, and Paulo Laerte Natti. "Numerical convergence of a Telegraph Predator-Prey system." Semina: Ciências Exatas e Tecnológicas 43, no. 1Esp (2022): 51–66. http://dx.doi.org/10.5433/1679-0375.2022v43n1espp51.

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Numerical convergence of a Telegraph Predator-Prey system is studied. This partial differential equation (PDE) system can describe various biological systems with reactive, diffusive, and delay effects. Initially, the PDE system was discretized by the Finite Differences method. Then, a system of equations in a time-explicit form and in a space-implicit form was obtained. The consistency of the Telegraph Predator-Prey system discretization was verified. Von Neumann stability conditions were calculated for a Predator-Prey system with reactive terms and for a Delayed Telegraph system. On the othe

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12

Erkurşun Özcan, Nazife. "On ergodic properties of operator nets on the predual of von neumann algebras." Studia Scientiarum Mathematicarum Hungarica 55, no. 4 (2018): 479–86. http://dx.doi.org/10.1556/012.2018.55.4.1414.

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In this paper, we proved theorems which give the conditions that special operator nets on a predual of von Neumann algebras are strongly convergent under the Markov case. Moreover, we investigate asymptotic stability and existence of a lower-bound function for such nets.

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13

Fukuyo, Kazuhiro. "Conditional stability of Larkin methods with non-uniform grids." Theoretical and Applied Mechanics 37, no. 2 (2010): 139–59. http://dx.doi.org/10.2298/tam1002139f.

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Stability analysis based on the von Neumann method showed that the Larkin methods for two-dimensional heat conduction with non- uniform grids are conditionally stable while they are known to be unconditionally stable with uniform grids. The stability criteria consisting of the dimensionless time step ?t, the space intervals ?x, ?y, and the ratios of neighboring space intervals ?, ? were derived from the stability analysis. A subsequent numerical experiment demonstrated that solutions derived by the Larkin methods with non-uniform grids lose stability and accuracy when the criteria are not sati

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14

Larkin, Eugene, Alexey Bogomolov, and Sergey Feofilov. "Stability of digital feedback control systems." MATEC Web of Conferences 161 (2018): 02004. http://dx.doi.org/10.1051/matecconf/201816102004.

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Specific problems arising, when Von Neumann type computer is used as feedback element, are considered. It is shown, that due to specifics of operation this element introduce pure lag into control loop, and lag time depends on complexity of algorithm of control. Method of evaluation of runtime between reading data from sensors of object under control and write out data to actuator based on the theory of semi- Markov process is proposed. Formulae for time characteristics estimation are obtained. Lag time characteristics are used for investigation of stability of linear systems. Digital PID contr

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15

Krivovichev, Gerasim Vladimirovich. "On the stability of lattice boltzmann equations for one-dimensional diffusion equation." International Journal of Modeling, Simulation, and Scientific Computing 08, no. 01 (2017): 1750013. http://dx.doi.org/10.1142/s1793962317500131.

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Stability analysis of lattice Boltzmann equations (LBEs) on initial conditions for one-dimensional diffusion is performed. Stability of the solution of the Cauchy problem for the system of linear Bhatnaghar–Gross–Krook kinetic equations is demonstrated for the cases of D1Q2 and D1Q3 lattices. Stability of the scheme for D1Q2 lattice is analytically analyzed by the method of differential approximation. Stability of parametrical scheme is numerically investigated by von Neumann method in parameter space. As a result of numerical analysis, the correction of the hypothesis on transfer of stability

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16

Lezani, Nadine Mulya, and Ummu Habibah. "Numerical Solution of Burgers Equation using Cubic B-Spline Collocation Method and Neumann Boundary Condition." Indonesian Journal of Mathematics and Applications 1, no. 2 (2023): 25–34. http://dx.doi.org/10.21776/ub.ijma.2023.001.02.3.

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Burgers equation is one of the nonlinear differential equations which is generally difficult to determine its analytical solution, so it is necessary to do a numerical approach. This article discusses the numerical solution of the Burgers equation using the Cubic B-Spline Collocation method. The first step is to derive the numerical scheme using the Cubic B-Spline Collocation method for the space variable and the Crank-Nicholson method for the time variable. Furthermore, based on von Neumann stability analysis, it is obtained that the numerical scheme of Burgers equation is unconditionally sta

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17

Castillo, Paul, and Sergio Gómez. "Análisis de Von Neumann para el métodoLocal Discontinuous Galerkin en 1D." Revista Integración 37, no. 2 (2019): 199–217. http://dx.doi.org/10.18273/revint.v37n2-2019001.

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Using the von Neumann analysis as a theoretical tool, an analysisof the stability conditions of some explicit time marching schemes, in com-bination with the spatial discretizationLocal Discontinuous Galerkin(LDG)and high order approximations, is presented. The stabilityconstant, CFL(Courant-Friedrichs-Lewy), is studied as a function of theLDG parametersand the approximation degree. A series of numerical experiments is carriedout to validate the theoretical results.

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18

Raed, Raed. "On The Numerical Solutions of the Neutrosophic One-Dimensional Sine-Gordon System." International Journal of Neutrosophic Science 25, no. 1 (2025): 25–36. http://dx.doi.org/10.54216/ijns.250303.

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This paper uses finite difference methods to study the numerical solution for neutrosophic Sine-Gordon system in one dimension. We use the explicit method and Crank-Nicholson method. Also, an effective comparison between the results of the two methods has been made, where we obtain the result that Crank-Nicholson method is more accurate than the explicit method, but the explicit method is easier. We also study the stability analysis for each method by using Fourier (Von-Neumann) method and get that Crank-Nicholson method is unconditionally stable while the Explicit method is stable under the c

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19

Owino, Benard, Fredrick Nyamwala, and David Ambogo. "Stability of Krein-von Neumann self-adjoint operator extension under unbounded perturbations." Annals of Mathematics and Computer Science 23 (April 26, 2024): 29–47. http://dx.doi.org/10.56947/amcs.v23.300.

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We have considered a fourth order difference operator defined on the Hilbert space of square summable sequences on N. We investigated the stability of existence of Krein-von Neumann self-adjoint extension of difference operators under bounded and unbounded coefficients. Using asymptotic summation based on discretised Levinson's theorem and appropriate smoothness and decay conditions, we have shown that unlike the case of deficiency indices and discrete spectrum, the existence of positive self-adjoint operator extensions is stable under unbounded perturbations. These results now exhaustively ch

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20

Liu, Yingfan. "An Optimal Lower Eigenvalue System." Abstract and Applied Analysis 2011 (2011): 1–20. http://dx.doi.org/10.1155/2011/208624.

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An optimal lower eigenvalue system is studied, and main theorems including a series of necessary and suffcient conditions concerning existence and a Lipschitz continuity result concerning stability are obtained. As applications, solvability results to some von-Neumann-type input-output inequalities, growth, and optimal growth factors, as well as Leontief-type balanced and optimal balanced growth paths, are also gotten.

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21

Mousa, Mohamed M., and Wen-Xiu Ma. "Efficient modeling of shallow water equations using method of lines and artificial viscosity." Modern Physics Letters B 34, no. 04 (2019): 2050051. http://dx.doi.org/10.1142/s0217984920500517.

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In this work, two numerical schemes were developed to overcome the problem of shock waves that appear in the solutions of one/two-layer shallow water models. The proposed numerical schemes were based on the method of lines and artificial viscosity concept. The robustness and efficiency of the proposed schemes are validated on many applications such as dam-break problem and the problem of interface propagation of two-layer shallow water model. The von Neumann stability of proposed schemes is studied and hence, the sufficient condition for stability is deduced. The results were presented graphic

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22

PAN, X. F., AIGUO XU, GUANGCAI ZHANG, and SONG JIANG. "LATTICE BOLTZMANN APPROACH TO HIGH-SPEED COMPRESSIBLE FLOWS." International Journal of Modern Physics C 18, no. 11 (2007): 1747–64. http://dx.doi.org/10.1142/s0129183107011716.

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We present an improved lattice Boltzmann model for high-speed compressible flows. The model is composed of a discrete-velocity model by Kataoka and Tsutahara15 and an appropriate finite-difference scheme combined with an additional dissipation term. With the dissipation term parameters in the model can be flexibly chosen so that the von Neumann stability condition is satisfied. The influence of the various model parameters on the numerical stability is analyzed and some reference values of parameter are suggested. The new scheme works for both subsonic and supersonic flows with a Mach number u

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23

Agnes, Agnes. "On the Numerical Solutions Based On Exponential Finite Difference Method for Kuramoto-Sivashinsky Equation and Numerical Stability Analysis." Neutrosophic and Information Fusion 4, no. 2 (2024): 30–44. http://dx.doi.org/10.54216/nif.040204.

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In this paper, we solve the Kuramoto-Sivashinsky Equation numerically by finite-difference methods, using two different schemes which are the Fully Implicit scheme and Exponential finite difference scheme, because of the existence of the fourth derivative in the equation we suggested a treatment for the numerical solution of the two previous scheme by parting the mesh grid into five regions, the first region represents the first boundary condition, the second at the grid point x1, while the third represents the grid points x2,x3,…xn-2, the fourth represents the grid point xn-1 and the fifth is

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24

O’Brien, Gareth S. "3D rotated and standard staggered finite-difference solutions to Biot’s poroelastic wave equations: Stability condition and dispersion analysis." GEOPHYSICS 75, no. 4 (2010): T111—T119. http://dx.doi.org/10.1190/1.3432759.

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A fourth-order in space and second-order in time 3D staggered (SG) and rotated-staggered-grid (RSG) method for the solution of Biot’s equation are presented. The numerical dispersion and stability conditions are derived using a von Neumann analysis. The exact stability condition is calculated from the roots of a 12th-order polynomial and therefore no nontrivial expression exists. To overcome this, a 1D stability condition is usually generalized to three dimensions. It is shown that in certain cases, the 1D approximate stability condition is violated by a 3D SG method. The RSG method obeys the

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25

Kim, Dojin. "A Modified PML Acoustic Wave Equation." Symmetry 11, no. 2 (2019): 177. http://dx.doi.org/10.3390/sym11020177.

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In this paper, we consider a two-dimensional acoustic wave equation in an unbounded domain and introduce a modified model of the classical un-split perfectly matched layer (PML). We apply a regularization technique to a lower order regularity term employed in the auxiliary variable in the classical PML model. In addition, we propose a staggered finite difference method for discretizing the regularized system. The regularized system and numerical solution are analyzed in terms of the well-posedness and stability with the standard Galerkin method and von Neumann stability analysis, respectively.

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26

Lines, Larry R., Raphael Slawinski, and R. Phillip Bording. "A recipe for stability of finite‐difference wave‐equation computations." GEOPHYSICS 64, no. 3 (1999): 967–69. http://dx.doi.org/10.1190/1.1444605.

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Finite‐difference solutions to the wave equation are pervasive in the modeling of seismic wave propagation (Kelly and Marfurt, 1990) and in seismic imaging (Bording and Lines, 1997). That is, they are useful for the forward problem (modeling) and the inverse problem (migration). In computational solutions to the wave equation, it is necessary to be aware of conditions for numerical stability. In this short note, we examine a convenient recipe for insuring stability in our finite‐difference solutions to the wave equation. The stability analysis for finite‐difference solutions of partial differe

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27

Todor, Radu, Ionuţ Chiose, and George Marinescu. "Morse inequalities for covering manifolds." Nagoya Mathematical Journal 163 (September 2001): 145–65. http://dx.doi.org/10.1017/s0027763000007947.

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We study the existence of L2 holomorphic sections of invariant line bundles over Galois coverings. We show that the von Neumann dimension of the space of L2 holomorphic sections is bounded below under weak curvature conditions. We also give criteria for a compact complex space with isolated singularities and some related strongly pseudoconcave manifolds to be Moishezon. As applications we prove the stability of the previous Moishezon pseudoconcave manifolds under perturbation of complex structures as well as weak Lefschetz theorems.

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28

Hutchinson, A. J., C. Harley, and E. Momoniat. "Numerical Investigation of the Steady State of a Driven Thin Film Equation." Journal of Applied Mathematics 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/181939.

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A third-order ordinary differential equation with application in the flow of a thin liquid film is considered. The boundary conditions come from Tanner's problem for the surface tension driven flow of a thin film. Symmetric and nonsymmetric finite difference schemes are implemented in order to obtain steady state solutions. We show that a central difference approximation to the third derivative in the model equation produces a solution curve with oscillations. A difference scheme based on a combination of forward and backward differences produces a smooth accurate solution curve. The stability

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29

BHATTACHARYA, ANINDYA, and AMIT K. BISWAS. "STABILITY OF THE CORE IN A CLASS OF NTU GAMES: A CHARACTERIZATION." International Game Theory Review 04, no. 02 (2002): 165–72. http://dx.doi.org/10.1142/s0219198902000628.

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The core and the stable set are possibly the two most crucially important solution concepts for cooperative games. The relation between the two has been investigated in the context of symmetric transferable utility games and this has been related to the notion of large core. In this paper the relation between the von-Neumann–Morgenstern stability of the core and the largeness of it is investigated in the case of non-transferable utility (NTU) games. The main findings are that under certain regularity conditions, if the core of an NTU game is large then it is a stable set and for symmetric NTU

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30

Kedir, Aliyi, and Muleta Hailu. "Numerical Method of the Line for Solving One Dimensional Initial- Boundary Singularly Perturbed Burger Equation." Indian Journal of Advanced Mathematics (IJAM) 1, no. 2 (2021): 4–14. https://doi.org/10.54105/ijam.B1103.101221.

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In this Research Method of Line is used to find the approximation solution of one dimensional singularly perturbed Burger equation given with initial and boundary conditions. First, the given solution domain is discretized and the derivative involving the spatial variable x is replaced into the functional values at each grid points by using the central finite difference method. Then, the resulting first-order linear ordinary differential equation is solved by the fifth-order Runge-Kutta method. To validate the applicability of the proposed method, one model example is considered and solved for

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31

Mugheri, Abdul Qadir. "Numerical Simulation of One-Dimensional Advection Diffusion Equation by New Hybrid Explicit Finite Difference Schemes." Volume 21, Issue 1 21, no. 1 (2023): 54–62. http://dx.doi.org/10.52584/qrj.2101.07.

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In this paper, the aim is to develop two Hybrid Explicit Schemes based on the Finite Difference method for a one- dimensional Advection Diffusion Equation. Moreover, the study considered the advection-diffusion equation as an initial boundary value problem (IBVP) for numerical solutions obtained from various second-order explicit methods along with the solution by proposed methods. Von-Neumann stability analysis is used to analyze the stability of the developed schemes graphically. In the numerical analysis of errors, the L 2 has been computed to compare proposed methods with existing methods

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32

Nawaz, Yasir, Muhammad Shoaib Arif, Wasfi Shatanawi, and Muhammad Usman Ashraf. "A Fourth Order Numerical Scheme for Unsteady Mixed Convection Boundary Layer Flow: A Comparative Computational Study." Energies 15, no. 3 (2022): 910. http://dx.doi.org/10.3390/en15030910.

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In this paper, a three-stage fourth-order numerical scheme is proposed. The first and second stages of the proposed scheme are explicit, whereas the third stage is implicit. A fourth-order compact scheme is considered to discretize space-involved terms. The stability of the fourth-order scheme in space and time is checked using the von Neumann stability criterion for the scalar case. The stability region obtained by the scheme is more than the one given by explicit Runge–Kutta methods. The convergence conditions are found for the system of partial differential equations, which are non-dimensio

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GROGGER, HERWIG A. "OPTIMIZED ARTIFICIAL DISSIPATION TERMS FOR ENHANCED STABILITY LIMITS." Journal of Computational Acoustics 15, no. 02 (2007): 235–53. http://dx.doi.org/10.1142/s0218396x07003329.

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Finite difference approximations for the convection equation are developed, which exhibit enhanced stability limits for explicit Runge–Kutta integration. Stability limits are increased by adding artificial dissipation terms, which are optimized to yield greatest stable time steps. For the artificial dissipation terms, symmetric finite difference approximations of even-order derivatives are used with differencing stencils equal to the convective stencils. The spatial discretization inclusive of the added dissipation term is shown to be consistent with a first derivative. The formal order of acc

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Zhang, Yuxuan, and Dingxi Wang. "Numerical stability analysis of solution methods for steady and harmonic balance equations." Journal of the Global Power and Propulsion Society 9 (March 3, 2025): 1–18. https://doi.org/10.33737/jgpps/193865.

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This study investigates the stability and convergence properties of solution methods for the steady and unsteady Euler equations. A central scheme with artificial dissipation is used for spatial discretization. A Runge-Kutta scheme is used for the pseudo-time integration. The implicit residual smoothing for steady and harmonic balance solutions is achieved using the Lower-Upper Symmetric Gauss-Seidel(LU-SGS) method and the Lower-Upper Symmetric Gauss-Seidel/Block Jacobi(LU-SGS/BJ) method, respectively. Both the von Neumann and matrix methods are used to analyze the stability of the involved so

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35

Redouane, Kelthoum Lina, Nouria Arar, Abdellatif Ben Makhlouf, and Abeer Alhashash. "A Higher-Order Improved Runge–Kutta Method and Cubic B-Spline Approximation for the One-Dimensional Nonlinear RLW Equation." Mathematical Problems in Engineering 2023 (April 19, 2023): 1–13. http://dx.doi.org/10.1155/2023/4753873.

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This article developed a significant improvement of a Galerkin-type approximation to the regularized long-wave equation (RLW) solution under homogeneous Dirichlet boundary conditions for achieving higher accuracy in time variables. First, a basis derived from cubic B-splines and limit conditions is used to perform a Galerkin-type approximation. Then, a Crank–Nicolson and fourth-order 4-stage improved Runge–Kutta scheme (IRK4) is used to discretize time. Both a strong stability analysis of a fully discrete IRK4 scheme and the evaluation of Von Neumann stability of the proposed Crank–Nicolson te

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36

Al-Khateeb, Areen. "Efficient Numerical Solutions for Fuzzy Time Fractional Convection Diffusion Equations Using Two Explicit Finite Difference Methods." Axioms 13, no. 4 (2024): 221. http://dx.doi.org/10.3390/axioms13040221.

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In this study, we explore fractional partial differential equations as a more generalized version of classical partial differential equations. These fractional equations have shown promise in providing improved descriptions of certain phenomena under specific circumstances. The main focus of this paper comprises the development, analysis, and application of two explicit finite difference schemes to solve an initial boundary value problem involving a fuzzy time fractional convection–diffusion equation with a fractional order in the range of 0≤ ξ ≤ 1. The uniqueness of this problem lies in its c

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Momoniat, E., M. M. Rashidi, and R. S. Herbst. "Numerical Investigation of Thin Film Spreading Driven by Surfactant Using Upwind Schemes." Mathematical Problems in Engineering 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/325132.

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Numerical solutions of a coupled system of nonlinear partial differential equations modelling the effects of surfactant on the spreading of a thin film on a horizontal substrate are investigated. A CFL condition is obtained from a von Neumann stability analysis of a linearised system of equations. Numerical solutions obtained from a Roe upwind scheme with a third-order TVD Runge-Kutta approximation to the time derivative are compared to solutions obtained with a Roe-Sweby scheme coupled to a minmod limiter and a TVD approximation to the time derivative. Results from both of these schemes are c

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38

Yokuş, Asıf. "Truncation and convergence dynamics: KdV Burgers model in the sense of Caputo derivative." Boletim da Sociedade Paranaense de Matemática 40 (January 26, 2022): 1–7. http://dx.doi.org/10.5269/bspm.47472.

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This study examines the time fractional KdV Burgers equation with the initial conditions by using the extended result on Caputo formula, finite difference method (FDM). For this reason, various fractional differential operators are defined and analyzed. In order to check the stability of the numerical scheme, the Fourier-von Neumann technique is used. By presenting an example of KdV Burgers equation above mentioned issues are discussed and numerical solutions of the error estimates have been found for the FDM. For the errors in $L_2$ and $L_\infty$ the method accuracy has been controlled. More

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Baber, Muhammad Zafarullah, Nauman Ahmed, Muhammad Waqas Yasin, et al. "Comparisons of Numerical and Solitary Wave Solutions for the Stochastic Reaction–Diffusion Biofilm Model including Quorum Sensing." Mathematics 12, no. 9 (2024): 1293. http://dx.doi.org/10.3390/math12091293.

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This study deals with a stochastic reaction–diffusion biofilm model under quorum sensing. Quorum sensing is a process of communication between cells that permits bacterial communication about cell density and alterations in gene expression. This model produces two results: the bacterial concentration, which over time demonstrates the development and decomposition of the biofilm, and the biofilm bacteria collaboration, which demonstrates the potency of resistance and defense against environmental stimuli. In this study, we investigate numerical solutions and exact solitary wave solutions with t

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Aliyi, Kedir, and Hailu Muleta. "Numerical Method of the Line for Solving One Dimensional Initial- Boundary Singularly Perturbed Burger Equation." Indian Journal of Advanced Mathematics 1, no. 2 (2021): 4–14. http://dx.doi.org/10.35940/ijam.b1103.101221.

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In this Research Method of Line is used to find the approximation solution of one dimensional singularly perturbed Burger equation given with initial and boundary conditions. First, the given solution domain is discretized and the derivative involving the spatial variable x is replaced into the functional values at each grid points by using the central finite difference method. Then, the resulting first-order linear ordinary differential equation is solved by the fifth-order Runge-Kutta method. To validate the applicability of the proposed method, one model example is considered and solved for

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Aliyi, Kedir, and Hailu Muleta. "Numerical Method of the Line for Solving One Dimensional Initial- Boundary Singularly Perturbed Burger Equation." Indian Journal of Advanced Mathematics 1, no. 2 (2021): 4–14. http://dx.doi.org/10.54105/ijam.b1103.101221.

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In this Research Method of Line is used to find the approximation solution of one dimensional singularly perturbed Burger equation given with initial and boundary conditions. First, the given solution domain is discretized and the derivative involving the spatial variable x is replaced into the functional values at each grid points by using the central finite difference method. Then, the resulting first-order linear ordinary differential equation is solved by the fifth-order Runge-Kutta method. To validate the applicability of the proposed method, one model example is considered and solved for

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Morrow, Richard. "An Implicit Flux-Corrected Transport Algorithm Used for Gas Discharge Calculations." Plasma 8, no. 1 (2025): 7. https://doi.org/10.3390/plasma8010007.

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An implicit flux-corrected transport (FCT) and diffusion algorithm was developed and used in many gas discharge calculations. Such calculations require the use of a fine mesh where the electric field changes rapidly; that is, near electrodes or in a streamer front. If diffusion is included using an explicit method, then the von Neumann stability condition severely limits the time-step that can be used; however, this limitation does not apply to implicit methods. Further, for gas discharge calculations including space-charge effects, it is necessary to solve the continuity equations with no neg

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Fournié, Michel, and Alain Rigal. "High Order Compact Schemes in Projection Methods for Incompressible Viscous Flows." Communications in Computational Physics 9, no. 4 (2011): 994–1019. http://dx.doi.org/10.4208/cicp.230709.080710a.

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AbstractWithin the projection schemes for the incompressible Navier-Stokes equations (namely “pressure-correction” method), we consider the simplest method (of order one in time) which takes into account the pressure in both steps of the splitting scheme. For this scheme, we construct, analyze and implement a new high order compact spatial approximation on nonstaggered grids. This approach yields a fourth order accuracy in space with an optimal treatment of the boundary conditions (without error on the velocity) which could be extended to more general splitting. We prove the unconditional stab

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Sochacki, James, Robert Kubichek, John George, W. R. Fletcher, and Scott Smithson. "Absorbing boundary conditions and surface waves." GEOPHYSICS 52, no. 1 (1987): 60–71. http://dx.doi.org/10.1190/1.1442241.

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One of the major problems in numerically simulating waves traveling in the Earth is that an artificial boundary must be introduced to produce unique solutions. To eliminate the spurious reflections introduced by this artificial boundary, we use a damping expression based on analogies to shock absorbers. This method can reduce the amplitude of the reflected wave to any pre‐specified value and is successful for waves at any angle of incidence. The method can eliminate unwanted reflections from the surface, reflections at the corners of the model, and waves reflected off an interface that strike

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Ginzburg, Irina. "Truncation Errors, Exact And Heuristic Stability Analysis Of Two-Relaxation-Times Lattice Boltzmann Schemes For Anisotropic Advection-Diffusion Equation." Communications in Computational Physics 11, no. 5 (2012): 1439–502. http://dx.doi.org/10.4208/cicp.211210.280611a.

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AbstractThis paper establishes relations between the stability and the high-order truncated corrections for modeling of the mass conservation equation with the two-relaxation-times (TRT) collision operator. First we propose a simple method to derive the truncation errors from the exact, central-difference type, recurrence equations of the TRT scheme. They also supply its equivalent three-time-level discretization form. Two different relationships of the two relaxation rates nullify the third (advection) and fourth (pure diffusion) truncation errors, for any linear equilibrium and any velocity

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Huntul, M. J. "Recovering a source term in the higher-order pseudo-parabolic equation via cubic spline functions." Physica Scripta 97, no. 3 (2022): 035004. http://dx.doi.org/10.1088/1402-4896/ac54d0.

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Abstract In this paper, we considered an inverse problem of recovering the space-dependent source coefficient in the third-order pseudo-parabolic equation from final over-determination condition. This inverse problem appears extensively in the modelling of various phenomena in physics such as the motion of non-Newtonian fluids, thermodynamic processes, filtration in a porous medium, etc. The unique solvability theorem for this inverse problem is supplied. However, since the governing equation is yet ill-posed (very slight errors in the final input may cause relatively significant errors in the

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Ahmed, Sherwan S., and Bewar A. Mahmood. "A Bicubic trigonometric B-Spline Approach for Solving the Nonlinear Generalized 2D Burger's Equation." International Journal of Analysis and Applications 23 (June 16, 2025): 142. https://doi.org/10.28924/2291-8639-23-2025-142.

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Nonlinear reaction-diffusion problems, such as the nonlinear generalized two-dimensional Burgers’ equation, play a crucial role in various fields, including developmental biology, population dynamics, engineering, and physics. This study focuses on the numerical solution of the two-dimensional Burgers’ equation using a collocation method based on bicubic trigonometric B-spline functions combined with a θ-weighted scheme. The spatial and temporal domains are discretized using bicubic trigonometric B-spline functions and a finite difference approach, respectively. The nonlinear terms in the equa

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Devi, Rekha, and Shilpa Sood. "Numerical Investigation of Three-Dimensional Magnetohydrodynamic Flow of Ag 􀀀 H2O Nanofluid Over an Oscillating Surface in a Rotating Porous Medium." Indian Journal Of Science And Technology 17, no. 8 (2024): 679–90. http://dx.doi.org/10.17485/ijst/v17i8.2892.

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Objective: To investigate the three-dimensional flow of a nanofluid (Ag-water) over a stretchable vertical oscillatory sheet. This study involves considering fluctuating temperatures on the sheet and comparing them to the free stream temperature. The formulation of the unsteady boundary layer equations leading to the flow of nanofluid also takes into consideration the occurrence of the heterogeneous-homogeneous chemical reaction and thermal radiation. Method: The governing equations and the boundary conditions have been derived in a dimensionless form by using the appropriate transformations,

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Yokus, Asif, Bülent Kuzu, and Uğur Demiroğlu. "Investigation of solitary wave solutions for the (3 + 1)-dimensional Zakharov–Kuznetsov equation." International Journal of Modern Physics B 33, no. 29 (2019): 1950350. http://dx.doi.org/10.1142/s0217979219503508.

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In this paper, the new traveling wave solutions containing the trigonometric functions, hyperbolic functions and rational functions of [Formula: see text]-dimensional Zakharov–Kuznetsov equation are obtained. The graphs of the solution functions are presented by giving specific values to the constants. Numerical solutions are obtained by using finite difference method with new initial condition. Von Neumann’s Stability, Consistency and Linear Stability analysis of the equation are performed and [Formula: see text], [Formula: see text] norm errors are also examined with the truncation error. Th

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SHORT, M., I. I. ANGUELOVA, T. D. ASLAM, J. B. BDZIL, A. K. HENRICK, and G. J. SHARPE. "Stability of detonations for an idealized condensed-phase model." Journal of Fluid Mechanics 595 (January 8, 2008): 45–82. http://dx.doi.org/10.1017/s0022112007008750.

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The stability of travelling wave Chapman–Jouguet and moderately overdriven detonations of Zeldovich–von Neumann–Döring type is formulated for a general system that incorporates the idealized gas and condensed-phase (liquid or solid) detonation models. The general model consists of a two-component mixture with a one-step irreversible reaction between reactant and product. The reaction rate has both temperature and pressure sensitivities and has a variable reaction order. The idealized condensed-phase model assumes a pressure-sensitive reaction rate, a constant-γ caloric equation of state for an

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