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Journal articles on the topic 'Quasi Linear Equation'

Author: Grafiati

Published: 27 January 2023

Last updated: 25 July 2025

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1

Yermachenko, I. "MULTIPLE SOLUTIONS OF THE FOURTH‐ORDER EMDEN‐FOWLER EQUATION." Mathematical Modelling and Analysis 11, no. 3 (2006): 347–56. http://dx.doi.org/10.3846/13926292.2006.9637322.

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Two-point boundary value problems for the fourth-order Emden-Fowler equation are considered. If the given equation can be reduced to a quasi‐linear one with a non‐resonant linear part so that both equations are equivalent in some domain D, and if solution of the quasi‐linear problem is located in D, then the original problem has a solution. We show that a quasi‐linear problem has a solution of definite type which corresponds to the type of the linear part. If quasilinearization is possible for essentially different linear parts, then the original problem has multiple solutions.

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2

FRICKE, J. ROBERT. "QUASI-LINEAR ELASTODYNAMIC EQUATIONS FOR FINITE DIFFERENCE SOLUTIONS IN DISCONTINUOUS MEDIA." Journal of Computational Acoustics 01, no. 03 (1993): 303–20. http://dx.doi.org/10.1142/s0218396x93000160.

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The linear elastodynamic equations are ill-posed for models which contain high contrast density discontinuities. This paper presents a quasi-linear superset of the linear equations that is well-posed for this situation. The extended system contains a conservation of mass equation and a quasi-linear convective term in the momentum equation. Density, momentum, and stress are the field variables in the quasi-linear system, which is cast in a first order form. Using a Lax–Wendroff finite difference approximation, the utility of the quasi-linear system is demonstrated by modeling underwater acousti

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3

Yaremenko, Mikola Ivanovich. "QUASI-LINEAR EVOLUTION AND ELLIPTIC EQUATIONS." Journal of Progressive Research in Mathematics 11, no. 3 (2017): 1645–69. https://doi.org/10.5281/zenodo.3975990.

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In this article we use a new type of nonlinear elliptic operators that are associated with left side of elliptic equation and studied their properties. We draw up the form, that is associated with non-linear elliptic operator studying the properties this operator by means of form. We proved some a prior estimates which are theorems about properties of solutions under certain conditions on the function that forming this equation. We proved the existence of solution of quasi-linear evolution equation with singular coefficients in , l R l  >2 space by Galerkin method and showed that

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4

Everitt, W. N. "A note on linear ordinary quasi-differential equations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 101, no. 1-2 (1985): 1–14. http://dx.doi.org/10.1017/s0308210500026111.

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SynopsisThe theory of differential equations is largely concerned with properties of solutions of individual, or classes of, equations. This paper is given over to the converse problem - that of seeking properties of functions which require them to be, in some respect, solutions of a differential equation, and to determining all possible such differential equations.From this point of view this paper discusses only linear ordinary quasi-differential equations of the second order. However, the methods can be extended to quasi-differential equations of general order.

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5

Fu, Zhongjun, Jianyu Wang, Yun Ou, Genyuan Zhou, and Xiaorong Zhao. "A Linear-Correction Algorithm for Quasi-Synchronous DFT." Mathematical Problems in Engineering 2018 (December 27, 2018): 1–9. http://dx.doi.org/10.1155/2018/1268905.

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Spectral leakage in the harmonic measured by quasi-synchronous DFT (QSDFT) is mainly due to short-range leakage caused by deviation in the signal frequency. By analysing the short-range-leakage characteristic of QSDFT, a linear-correction algorithm (LCQS) for QSDFT’s harmonic-analysis results is proposed. LCQS contains two linear-correction equations: an amplitude-correction equation and an initial-phase-angle-correction equation. The former is constructed by the least-squares method, whereas the latter is generated based on the linear error characteristic of the QSDFT harmonic phase. Simulati

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6

Sun, Yingte, and Xiaoping Yuan. "Quasi-periodic solution of quasi-linear fifth-order KdV equation." Discrete & Continuous Dynamical Systems - A 38, no. 12 (2018): 6241–85. http://dx.doi.org/10.3934/dcds.2018268.

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7

Alnafisah, Yousef, Fahd Masood, Ali Muhib, and Osama Moaaz. "Improved Oscillation Theorems for Even-Order Quasi-Linear Neutral Differential Equations." Symmetry 15, no. 5 (2023): 1128. http://dx.doi.org/10.3390/sym15051128.

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In this study, our goal was to establish improved inequalities that enhance the asymptotic and oscillatory behaviors of solutions to even-order neutral differential equations. In the oscillation theory of neutral differential equations, the connection between the solution and its corresponding function plays a critical role. We refined these relationships by leveraging the modified monotonic properties of positive solutions and introduced new conditions that ensure the absence of positive solutions, confirming the oscillation of all solutions to the studied equation. Based on the concept of sy

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8

Belokursky, M. S. "Periodic and almost periodic solutions of the Riccati equations with linear reflecting function." Doklady of the National Academy of Sciences of Belarus 66, no. 5 (2022): 479–88. http://dx.doi.org/10.29235/1561-8323-2022-66-5-479-488.

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The method of Mironenko’s reflecting function is used for investigation of Riccati equations. The class of Riccati equations with certain-type reflecting function has been preliminarily constructed. The necessary and sufficient conditions, under which the Riccati equation would have a reflecting function linear in phase variable, are proved. These conditions are constructive in nature, since on their basis the formula is obtained, which shows the linear in phase variable reflecting function in terms of the coefficients of the Riccati equation. Additionally, the relationship between the parity

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9

Catino, Francesco, and Maria Maddalena Miccoli. "Construction of quasi-linear left cycle sets." Journal of Algebra and Its Applications 14, no. 01 (2014): 1550001. http://dx.doi.org/10.1142/s0219498815500012.

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In this paper, we produce a method to construct quasi-linear left cycle sets A with Rad (A) ⊆ Fix (A). Moreover, among these cycle sets, we give a complete description of those for which Fix (A) = Soc (A) and the underlying additive group is cyclic. Using such cycle sets, we obtain left non-degenerate involutive set-theoretic solutions of the Yang–Baxter equation which are different from those obtained in [P. Etingof, T. Schedler and A. Soloviev, Set-theoretical solutions to the quantum Yang–Baxter equation, Duke Math. J. 100 (1999) 169–209; P. Etingof, A. Soloviev and R. Guralnick, Indecompos

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10

Zhdanov, Michael S., Vladimir I. Dmitriev, Sheng Fang, and Gábor Hursán. "Quasi‐analytical approximations and series in electromagnetic modeling." GEOPHYSICS 65, no. 6 (2000): 1746–57. http://dx.doi.org/10.1190/1.1444859.

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The quasi‐linear approximation for electromagnetic forward modeling is based on the assumption that the anomalous electrical field within an inhomogeneous domain is linearly proportional to the background (normal) field through an electrical reflectivity tensor λ⁁. In the original formulation of the quasi‐linear approximation, λ⁁ was determined by solving a minimization problem based on an integral equation for the scattering currents. This approach is much less time‐consuming than the full integral equation method; however, it still requires solution of the corresponding system of linear equa

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11

Pivovarov, Michail L. "Steady-state solutions of Minorsky’s quasi-linear equation." Nonlinear Dynamics 106, no. 4 (2021): 3075–89. http://dx.doi.org/10.1007/s11071-021-06944-9.

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12

Maia, L. A., J. C. Oliveira Junior, and R. Ruviaro. "A quasi-linear Schrödinger equation with indefinite potential." Complex Variables and Elliptic Equations 61, no. 4 (2016): 574–86. http://dx.doi.org/10.1080/17476933.2015.1106483.

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13

Yan, Fangchi, and Qingtian Zhang. "Global solutions of quasi-linear Hamiltonian mKdV equation." Nonlinear Analysis 240 (March 2024): 113454. http://dx.doi.org/10.1016/j.na.2023.113454.

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14

Dikhaminjia, N., J. Rogava, and M. Tsiklauri. "Operator Splitting for Quasi-Linear Abstract Hyperbolic Equation." Journal of Mathematical Sciences 218, no. 6 (2016): 737–41. http://dx.doi.org/10.1007/s10958-016-3058-9.

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15

Paola, M. Di. "Linear Systems Excited by Polynomials of Filtered Poission Pulses." Journal of Applied Mechanics 64, no. 3 (1997): 712–17. http://dx.doi.org/10.1115/1.2788955.

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The stochastic differential equations for quasi-linear systems excited by parametric non-normal Poisson white noise are derived. Then it is shown that the class of memoryless transformation of filtered non-normal delta correlated process can be reduced, by means of some transformation, to quasi-linear systems. The latter, being excited by parametric excitations, are frst converted into ltoˆ stochastic differential equations, by adding the hierarchy of corrective terms which account for the nonnormality of the input, then by applying the Itoˆ differential rule, the moment equations have been de

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16

Zhang, Shenggang, Chungang Zhu, and Qinjiao Gao. "Numerical Solution of High-Dimensional Shockwave Equations by Bivariate Multi-Quadric Quasi-Interpolation." Mathematics 7, no. 8 (2019): 734. http://dx.doi.org/10.3390/math7080734.

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Radial basis function-based quasi-interpolation performs efficiently in high-dimensional approximation and its applications, which can attain the approximant and its derivatives directly without solving any large-scale linear system. In this paper, the bivariate multi-quadrics (MQ) quasi-interpolation is used to simulate two-dimensional (2-D) Burgers’ equation. Specifically, the spatial derivatives are approximated by using the quasi-interpolation, and the time derivatives are approximated by forward finite difference method. One advantage of the proposed scheme is its simplicity and easy impl

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17

Zhdanov, Michael S., Sheng Fang, and Gábor Hursán. "Electromagnetic inversion using quasi‐linear approximation." GEOPHYSICS 65, no. 5 (2000): 1501–13. http://dx.doi.org/10.1190/1.1444839.

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Three‐dimensional electromagnetic inversion continues to be a challenging problem in electrical exploration. We have recently developed a new approach to the solution of this problem based on quasi‐linear approximation of a forward modeling operator. It generates a linear equation with respect to the modified conductivity tensor, which is proportional to the reflectivity tensor and the complex anomalous conductivity. We solved this linear equation by using the regularized conjugate gradient method. After determining a modified conductivity tensor, we used the electrical reflectivity tensor to

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18

Carbonaro, P. "Exceptional hyperbolic systems of Hamiltonian form." European Journal of Applied Mathematics 6, no. 2 (1995): 157–67. http://dx.doi.org/10.1017/s0956792500001753.

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Some years ago, Bluman [1] gave the ‘integrability conditions’ for a linear second-order hyperbolic Equation, i.e. the conditions under which it can be mapped invertibly to a constant coefficient wave equation. Considering that a second-order hyperbolic equation in two dimensions can be regarded as the hodograph representation of a 2x2 quasi-linear homogeneous system, one may wonder how the fulfilment of the above-mentioned integrability conditions is reflected in the structure of the quasi-linear system. The question is especially interesting if the quasi-linear system derives from a Hamilton

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19

Alexandrikova, T. A., and M. P. Galanin. "NONLINEAR MONOTONIZATION OF THE BABENKO SCHEME FOR THE QUASI‐LINEAR ADVECTION EQUATION." Mathematical Modelling and Analysis 10, no. 2 (2005): 113–26. http://dx.doi.org/10.3846/13926292.2005.9637276.

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The paper is devoted to construction and development of new method for numerical solution of hyperbolic type equations [14, 17]. In the previous papers [4, 5, 6, 7, 8, 9] authors have investigated theoretically and tested experimentally 26 different finite‐difference schemes on 4 point patterns for the simplest hyperbolic equation: linear advection equation. This equation has the main features of every hyperbolic equation and is the important part of many mathematical models. In other cases the advection operator is the important part of the full operator of the problem. All 26 schemes have be

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20

Qaraad, Belgees, Osama Moaaz, Shyam Sundar Santra, Samad Noeiaghdam, Denis Sidorov, and Elmetwally M. Elabbasy. "Oscillatory Behavior of Third-Order Quasi-Linear Neutral Differential Equations." Axioms 10, no. 4 (2021): 346. http://dx.doi.org/10.3390/axioms10040346.

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In this paper, we consider a class of quasilinear third-order differential equations with a delay argument. We establish some conditions of such certain third-order quasi-linear neutral differential equation as oscillatory or almost oscillatory. Those criteria improve, complement and simplify a number of existing results in the literature. Some examples are given to illustrate the importance of our results.

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21

Malyshev, Igor. "On some perturbation techniques for quasi-linear parabolic equations." Journal of Applied Mathematics and Stochastic Analysis 3, no. 3 (1990): 169–75. http://dx.doi.org/10.1155/s1048953390000168.

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We study a nonhomogeneous quasi-linear parabolic equation and introduce a method that allows us to find the solution of a nonlinear boundary value problem in explicit form. This task is accomplished by perturbing the original equation with a source function, which is then found as a solution of some nonlinear operator equation.

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22

Wan, Renhui. "Long time stability for the dispersive SQG equation and Boussinesq equations in Sobolev space Hs." Communications in Contemporary Mathematics 22, no. 03 (2018): 1850063. http://dx.doi.org/10.1142/s0219199718500633.

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Dispersive SQG equation have been studied by many works (see, e.g., [M. Cannone, C. Miao and L. Xue, Global regularity for the supercritical dissipative quasi-geostrophic equation with large dispersive forcing, Proc. Londen. Math. Soc. 106 (2013) 650–674; T. M. Elgindi and K. Widmayer, Sharp decay estimates for an anisotropic linear semigroup and applications to the surface quasi-geostrophic and inviscid Boussinesq systems, SIAM J. Math. Anal. 47 (2015) 4672–4684; A. Kiselev and F. Nazarov, Global regularity for the critical dispersive dissipative surface quasi-geostrophic equation, Nonlineari

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23

BRIHAYE, Y., and PIOTR KOSINSKI. "QUASI-EXACTLY SOLVABLE RADIAL DIRAC EQUATIONS." Modern Physics Letters A 13, no. 18 (1998): 1445–52. http://dx.doi.org/10.1142/s0217732398001522.

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In the background of a central Coulomb potential, the Schrödinger and Dirac equations lead to exactly solvable spectral problems. When the Schrödinger–Coulomb equation is supplemented by a Harmonic potential, the corresponding spectral problem still possesses a finite number of algebraic solutions: it is quasi-exactly solvable. In this letter we analyze the spectral problem corresponding to the Dirac–Coulomb problem supplemented by a linear radial potential and we show that it also leads to quasi-exactly solvable equations.

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24

Kuznetsov, Ivan, and Sergey Sazhenkov. "Singular limits of the quasi-linear Kolmogorov-type equation with a source term." Journal of Hyperbolic Differential Equations 18, no. 04 (2021): 789–856. http://dx.doi.org/10.1142/s0219891621500247.

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Existence, uniqueness and stability of kinetic and entropy solutions to the boundary value problem associated with the Kolmogorov-type, genuinely nonlinear, degenerate hyperbolic–parabolic (ultra-parabolic) equation with a smooth source term is established. In addition, we consider the case when the source term contains a small positive parameter and collapses to the Dirac delta-function, as this parameter tends to zero. In this case, the limiting passage from the original equation with the smooth source to the impulsive ultra-parabolic equation is investigated and the formal limit is rigorous

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25

Selvaratnam, A. R., M. Vlieg-Hulstman, B. van-Brunt, and W. D. Halford. "On the solution of a class of second-order quasi-linear PDEs and the Gauss equation." ANZIAM Journal 42, no. 3 (2001): 312–23. http://dx.doi.org/10.1017/s1446181100011962.

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AbstractGauss' Theorema Egregium produces a partial differential equation which relates the Gaussian curvature K to components of the metric tensor and its derivatives. Well-known partial differential equations (PDEs) such as the Schrödinger equation and the sine-Gordon equation can be derived from Gauss' equation for specific choices of K and coördinate systems. In this paper we consider a class of Bäcklund Transformations which corresponds to coördinate transformations on surfaces with a given Gaussian curvature. These Bäcklund Transformations lead to the construction of solutions to certain

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26

Brozos-Vázquez, Miguel, Eduardo García-Río, Peter Gilkey, and Xabier Valle-Regueiro. "A natural linear equation in affine geometry: The affine quasi-Einstein Equation." Proceedings of the American Mathematical Society 146, no. 8 (2018): 3485–97. http://dx.doi.org/10.1090/proc/14090.

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27

Kohler, Simon, and Wolfgang Reichel. "Breather solutions for a quasi‐linear ‐dimensional wave equation." Studies in Applied Mathematics 148, no. 2 (2021): 689–714. http://dx.doi.org/10.1111/sapm.12455.

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28

Lyubanova, Anna Sh. "On an Inverse Problem for Quasi-Linear Elliptic Equation." Journal of Siberian Federal University. Mathematics & Physics 8, no. 1 (2015): 38–48. http://dx.doi.org/10.17516/1997-1397-2015-8-1-38-48.

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29

Takeuchi, Yoshiyuki. "Quasi-State Equation of Linear Systems with Time Delay." IEEJ Transactions on Electronics, Information and Systems 112, no. 4 (1992): 270–71. http://dx.doi.org/10.1541/ieejeiss1987.112.4_270.

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30

Donati-Martin, Catherine. "Quasi-Linear Elliptic Stochastic Partial Differential Equation: Markov property." Stochastics and Stochastic Reports 41, no. 4 (1992): 219–40. http://dx.doi.org/10.1080/17442509208833804.

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31

Rosenau, Philip. "Compact breathers in a quasi-linear Klein–Gordon equation." Physics Letters A 374, no. 15-16 (2010): 1663–67. http://dx.doi.org/10.1016/j.physleta.2010.01.065.

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32

Esposito, Pierpaolo. "A classification result for the quasi-linear Liouville equation." Annales de l'Institut Henri Poincaré C, Analyse non linéaire 35, no. 3 (2018): 781–801. http://dx.doi.org/10.1016/j.anihpc.2017.08.002.

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33

Ghosh, Tuhin, and Karthik Iyer. "Cloaking for a quasi-linear elliptic partial differential equation." Inverse Problems & Imaging 12, no. 2 (2018): 461–91. http://dx.doi.org/10.3934/ipi.2018020.

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34

Kapaev, A. A. "Quasi-linear Stokes phenomenon for the Painlevé first equation." Journal of Physics A: Mathematical and General 37, no. 46 (2004): 11149–67. http://dx.doi.org/10.1088/0305-4470/37/46/005.

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35

Squassina, Marco. "Boundary behavior for a singular quasi-linear elliptic equation." Journal of Mathematical Analysis and Applications 393, no. 2 (2012): 692–96. http://dx.doi.org/10.1016/j.jmaa.2012.04.023.

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36

Belan, E. P. "Quasi-periodic solutions of a linear functional-differential equation." Journal of Mathematical Sciences 82, no. 3 (1996): 3416–19. http://dx.doi.org/10.1007/bf02362656.

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37

Ravasoo, Arvi. "Modified constitutive equation for quasi-linear theory of viscoelasticity." Journal of Engineering Mathematics 78, no. 1 (2011): 111–18. http://dx.doi.org/10.1007/s10665-011-9473-5.

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38

Mohammad, Mutaz. "A Numerical Solution of Fredholm Integral Equations of the Second Kind Based on Tight Framelets Generated by the Oblique Extension Principle." Symmetry 11, no. 7 (2019): 854. http://dx.doi.org/10.3390/sym11070854.

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In this paper, we present a new computational method for solving linear Fredholm integral equations of the second kind, which is based on the use of B-spline quasi-affine tight framelet systems generated by the unitary and oblique extension principles. We convert the integral equation to a system of linear equations. We provide an example of the construction of quasi-affine tight framelet systems. We also give some numerical evidence to illustrate our method. The numerical results confirm that the method is efficient, very effective and accurate.

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39

Masood, Fahd, Osama Moaaz, Shyam Sundar Santra, U. Fernandez-Gamiz, and Hamdy A. El-Metwally. "Oscillation theorems for fourth-order quasi-linear delay differential equations." AIMS Mathematics 8, no. 7 (2023): 16291–307. http://dx.doi.org/10.3934/math.2023834.

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<abstract><p>In this paper, we deal with the asymptotic and oscillatory behavior of quasi-linear delay differential equations of fourth order. We first find new properties for a class of positive solutions of the studied equation, $ \mathcal{N}_{a} $. As an extension of the approach taken in <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup>, we establish a new criterion that guarantees that $ \mathcal{N}_{a} = \emptyset $. Then, we create a new oscillation criterion.</p></abstract>

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40

Jiao, Xiarong, Shan Jiang, and Hong Liu. "Nonlinear Moving Boundary Model of Low-Permeability Reservoir." Energies 14, no. 24 (2021): 8445. http://dx.doi.org/10.3390/en14248445.

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At present, there are two main methods for solving oil and gas seepage equations: analytical and numerical methods. In most cases, it is difficult to find the analytical solution, and the numerical solution process is complex with limited accuracy. Based on the mass conservation equation and the steady-state sequential substitution method, the moving boundary nonlinear equations of radial flow under different outer boundary conditions are derived. The quasi-Newton method is used to solve the nonlinear equations. The solutions of the nonlinear equations with an infinite outer boundary, constant

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41

Huang, Chen. "A variant of Clark’s theorem and its applications for nonsmooth functionals without the global symmetric condition." Advances in Nonlinear Analysis 11, no. 1 (2021): 285–303. http://dx.doi.org/10.1515/anona-2020-0197.

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Abstract We give a new non-smooth Clark’s theorem without the global symmetric condition. The theorem can be applied to generalized quasi-linear elliptic equations with small continous perturbations. Our results improve the abstract results about a semi-linear elliptic equation in Kajikiya [10] and Li-Liu [11].

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42

Feldman, Richard M., Bryan L. Deuermeyer, and Ciriaco Valdez-Flores. "Utilization of the method of linear matrix equations to solve a quasi-birth-death problem." Journal of Applied Probability 30, no. 3 (1993): 639–49. http://dx.doi.org/10.2307/3214772.

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The steady-state analysis of a quasi-birth-death process is possible by matrix geometric procedures in which the root to a quadratic matrix equation is found. A recent method that can be used for analyzing quasi-birth–death processes involves expanding the state space and using a linear matrix equation instead of the quadratic form. One of the difficulties of using the linear matrix equation approach regards the boundary conditions and obtaining the norming equation. In this paper, we present a method for calculating the boundary values and use the operator-machine interference problem as a ve

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43

Feldman, Richard M., Bryan L. Deuermeyer, and Ciriaco Valdez-Flores. "Utilization of the method of linear matrix equations to solve a quasi-birth-death problem." Journal of Applied Probability 30, no. 03 (1993): 639–49. http://dx.doi.org/10.1017/s0021900200044375.

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The steady-state analysis of a quasi-birth-death process is possible by matrix geometric procedures in which the root to a quadratic matrix equation is found. A recent method that can be used for analyzing quasi-birth–death processes involves expanding the state space and using a linear matrix equation instead of the quadratic form. One of the difficulties of using the linear matrix equation approach regards the boundary conditions and obtaining the norming equation. In this paper, we present a method for calculating the boundary values and use the operator-machine interference problem as a ve

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44

Cisneros-Ake, Luis A. "Quasi-steady state propagation in the davydov-type model with linear on-site interactions." Low Temperature Physics 48, no. 12 (2022): 1015–21. http://dx.doi.org/10.1063/10.0015110.

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The problem of electron transportation along a discrete deformable medium with linear on-site interactions in the Davydov approach is considered. It is found that the quasi-stationary state of the full equations of motion leads to a discrete nonlocal nonlinear Schrödinger (DNNLS) equation whose nonlocality is of the exponential type and depending on the on-site parameter. We use the variational approach to approximate discrete traveling wave solutions in the DNNLS equation. We find that the discrete solutions continued from the discrete nonlinear Schrödinger equation, corresponding to the vani

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45

Astashova, I. V. "ON OSCILLATION OF SOLUTIONS TO QUASI-LINEAR EMDEN – FOWLER TYPE HIGHER-ORDER DIFFERENTIAL EQUATIONS." Vestnik of Samara University. Natural Science Series 21, no. 6 (2017): 12–22. http://dx.doi.org/10.18287/2541-7525-2015-21-6-12-22.

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Existence and behavior of oscillatory solutions to nonlinear equations with regular and singular power nonlinearity are investigated. In particular, the existence of oscillatory solutions is proved for the equation y(n) + P(x; y; y ′ ; : : : ; y(n−1))|y|k sign y = 0; n 2; k ∈ R; k 1; P ̸= 0; P ∈ C(Rn+1): A criterion is formulated for oscillation of all solutions to the quasilinear even-order differential equation y(n) + nΣ−1 i=0 aj(x) y(i) + p(x) |y|ksigny = 0; p ∈ C(R); aj ∈ C(R); j = 0; : : : ; n − 1; k 1; n = 2m; m ∈ N; which generalizes the well-known Atkinson’s and Kiguradze’s criteria. T

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46

Makarov, V. L., and L. I. Demkiv. "Accuracy Estimates of Difference Schemes for Quasi-linear Parabolic Equations Taking into Account the Initial-boundary Effect." Computational Methods in Applied Mathematics 3, no. 4 (2003): 579–95. http://dx.doi.org/10.2478/cmam-2003-0036.

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AbstractFor difference schemes the initial-boundary problem for quasi-linear parabolic-type equations, ’a priori weight estimates’ of the error have been found. These estimates show how much the accuracy of difference schemes near the boundary of a time rectangle is higher than in the middle of it. Sufficient conditions of smoothness of the coefficients and the right-hand side of the quasi-linear parabolic equation and the initial conditions have been found. These conditions ensure a correctness of these a priori estimates.

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47

Izadi, Mohammad, Şuayip Yüzbaşi, and Samad Noeiaghdam. "Approximating Solutions of Non-Linear Troesch’s Problem via an Efficient Quasi-Linearization Bessel Approach." Mathematics 9, no. 16 (2021): 1841. http://dx.doi.org/10.3390/math9161841.

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Two collocation-based methods utilizing the novel Bessel polynomials (with positive coefficients) are developed for solving the non-linear Troesch’s problem. In the first approach, by expressing the unknown solution and its second derivative in terms of the Bessel matrix form along with some collocation points, the governing equation transforms into a non-linear algebraic matrix equation. In the second approach, the technique of quasi-linearization is first employed to linearize the model problem and, then, the first collocation method is applied to the sequence of linearized equations iterati

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48

Yoon, Peter H., Rodrigo A. López, Jungjoon Seough, et al. "Quasi-linear Analysis of Proton-cyclotron Instability." Astrophysical Journal 976, no. 2 (2024): 173. http://dx.doi.org/10.3847/1538-4357/ad86be.

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Abstract The proton-cyclotron (PC) instability operates in various space plasma environments. In the literature, the so-called velocity moment-based quasi-linear theory is employed to investigate the physical process of PC instability that takes place after the onset of early linear exponential growth. In this method, the proton velocity distribution function (VDF) is assumed to maintain a bi-Maxwellian form for all time, which substantially simplifies the analysis, but its validity has not been rigorously examined by comparing against the actual solution of the kinetic equation. The present p

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49

El Attaouy, Meryem, Khalil Ezzinbi, and Gaston Mandata ˜N'Guerekata. "Reduction principle for partial functional differential equation without compactness." Electronic Journal of Differential Equations 2023, no. 01-?? (2023): 39. http://dx.doi.org/10.58997/ejde.2023.39.

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This article establishes a reduction principle for partial functional differential equation without compactness of the semigroup generated by the linear part. Under conditions more general than the compactness of the C0-semigroup generated by the linear part, we establish the quasi-compactness of the C0-semigroup associated to the linear part of the partial functional differential equation. This result allows as to construct a reduced system that is posed by an ordinary differential equation posed in a finite dimensional space. Through this result we study the existence of almost automorphic a

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50

Torabi, K., H. Afshari, and E. Zafari. "Transverse Vibration of Non-Uniform Euler-Bernoulli Beam, Using Differential Transform Method (DTM)." Applied Mechanics and Materials 110-116 (October 2011): 2400–2405. http://dx.doi.org/10.4028/www.scientific.net/amm.110-116.2400.

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Analysis of transverse vibration of beams is presented in this paper. Unfortunately, complexities which appear in solving differential equation of transverse vibration of non-uniform beams, limit analytical solution to some special cases, so that the numerical method is presented. DTM is a numerical method for solving linear and some non-linear, ordinary and partial differential equations. In this paper, this technique has been applied for solving differential equation of transverse vibration of conical Euler-Bernoulli beam. Natural circular frequencies and mode shapes have been calculated. Co

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