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Journal articles on the topic 'Finite Differnce Methods'

Author: Grafiati

Published: 4 June 2025

Last updated: 1 August 2025

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1

S., Manna M. Sabawi and Y. Sabawi. "A Numerical Solution for Sine-Gordon Type System." System, Tikrit Journal of Pure Science 15, no. 3 (2010): 106–13. https://doi.org/10.5281/zenodo.3370232.

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Abstract  A numerical solution for Sine-Gordon type system was done by the use of two finite difference schemes, the first is the explicit scheme and the second is the Crank-Nicholson scheme. A comparison between the two schemes showed that the explicit scheme is easier and has faster convergence than the Crank-Nicholson scheme which is more accurate. The MATLAB environment  was used for the numerical computations.

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2

Amakobe James, Hagai. "Finite Difference Method Solution to Garlerkin's Finite Element Discretized Beam Equation." International Journal of Science and Research (IJSR) 10, no. 7 (2021): 635–38. https://doi.org/10.21275/sr21607193720.

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3

Kazhikenova, S. Sh. "FINITE DIFFERENCE METHOD IMPLEMENTATION FOR NUMERICALINTEGRATION HYDRODYNAMIC EQUATIONS MELTS." Eurasian Physical Technical Journal 17, no. 1 (2020): 145–50. http://dx.doi.org/10.31489/2020no1/145-150.

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4

Lakshmi, G. Yuva Roopa. "A Thorough Overview of Advancements in Finite Difference Methods for Differentiation." International Journal of Research Publication and Reviews 6, no. 3 (2025): 7499–503. https://doi.org/10.55248/gengpi.6.0325.12140.

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5

Dinh, Ta Van. "On multi-parameter error expansions in finite difference methods for linear Dirichlet problems." Applications of Mathematics 32, no. 1 (1987): 16–24. http://dx.doi.org/10.21136/am.1987.104232.

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6

Kobus, Jacek. "Finite-difference versus finite-element methods." Chemical Physics Letters 202, no. 1-2 (1993): 7–12. http://dx.doi.org/10.1016/0009-2614(93)85342-l.

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7

WU, Long, Michihisa TSUTAHARA, and Shinsuke TAJIRI. "631 Finite difference lattice Boltzmann method for incompressible flow using acceleration modification." Proceedings of The Computational Mechanics Conference 2006.19 (2006): 531–32. http://dx.doi.org/10.1299/jsmecmd.2006.19.531.

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8

Riza, Mustafa, Ali Özyapici, and Emine Misirli. "Multiplicative finite difference methods." Quarterly of Applied Mathematics 67, no. 4 (2009): 745–54. http://dx.doi.org/10.1090/s0033-569x-09-01158-2.

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9

Berzan, Vladimir. "COMPARATIVE ANALYSIS OF METHODS OF CALCULATION IN TRANSIENT AND WAVE PROCESSES IN ELECTRIC CIRCUITS." Journal of Engineering Science XXVI (2) (June 18, 2019): 40–57. https://doi.org/10.5281/zenodo.3249182.

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The problem of calculating the transient and wave processes in the circuits with the concentrated and distributed parameters is examined. A comparative-qualitative analysis of the analytical and numerical methods used for these purposes was carried out, indicating the advantages and disadvantages of their application. It is presented algorithms for applying the examined methods. It is found that numerical calculation methods have many advantages in studying stationary and dynamic processes in the natural sequence of processes course in the circuit. It is recommended to use the finite differenc

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10

Saeed, Rostam K., and Mohammed I. Sadeeq. "Numerical Solution of Nonlinear Whitham-Broer-Kaup Shallow Water Model Using Finite Difference Methods." Journal of Zankoy Sulaimani - Part A 19, no. 1 (2016): 197–210. http://dx.doi.org/10.17656/jzs.10597.

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11

Abdigaliyeva, А. N. "Modelling of the turbulent energy decay based on the finite-difference and spectral methods." International Journal of Mathematics and Physics 7, no. 1 (2016): 4–9. http://dx.doi.org/10.26577/2218-7987-2016-7-1-4-9.

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12

Ghuge, Vijaymala, T. L. Holambe, Bhausaheb Sontakke, and Gajanan Shrimangale. "Solving Time-fractional Order Radon Diffusion Equation in Water by Finite Difference Method." Indian Journal Of Science And Technology 17, no. 19 (2024): 1994–2001. http://dx.doi.org/10.17485/ijst/v17i19.868.

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Objective: The aim of this research is to gain a comprehensive understanding of radon diffusion equation in water. Methods: A time fractional radon diffusion equation with Caputo sense is employed to find diffusion dynamics of radon in water medium. The fractional order explicit finite difference technique is used to find its numerical solution. A Python software is used to find numerical solution. Findings: The effect of fractional-order parameters on the distribution and concentration profiles of radon in water has been investigated. Furthermore, we study stability and convergence of the exp

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13

Yadav, Ravi Kant. "Soret-Dufour effect on Unsteady MHD flow of Dusty viscoelastic fluid over inclined porous plate embedded in porous medium." International Journal of Science and Social Science Research 1, no. 1 (2023): 19–29. https://doi.org/10.5281/zenodo.13328094.

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In the current work, a continuously moving inclined plate with the Soret-Dufoureffect is subjected to an unstable two-dimensional MHD (Magnetohydro Dynamics) flow of adusty viscoelastic (Walter’s liquid model-B) incompressible viscous and electrically conductingfluid. The coupled equations involving a nonlinear problem are investigated using the CrankNicolson finite difference method, and a numerical solution for the velocity, temperature, andconcentration distributions is achieved.The graphical findings are shown to interpret the impact of the problem’s many significant parameters

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14

Abdukhamidov, Sardor, and Lobar Chorshanbiyeva. "SOLVING RESEARCH PROBLEMS OF FLOWS IN CHANNELS USING NUMERICAL METHODS." TECHNICAL SCIENCE RESEARCH IN UZBEKISTAN 2, no. 6 (2024): 142–45. https://doi.org/10.5281/zenodo.12548425.

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The study of fluid flow in channels is fundamental in various fields of engineering and environmental sciences. Traditional analytical methods often fall short in handling complex geometries and varying boundary conditions. Numerical methods have thus become indispensable in understanding and predicting fluid dynamics in channels. This paper explores the application of numerical methods in the study of flows in channels, focusing on the Finite Difference Method (FDM), Finite Element Method (FEM), and Computational Fluid Dynamics (CFD). Case studies and simulations are presented to illustrate t

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15

Ochilov, Sherali Baratovich, Gulrukh Djumanazarovna Khasanova, and Oisha Kurbanovna Khudayberdieva. "Method For Constructing Correlation Dependences For Functions Of Many Variables Used Finite Differences." American Journal of Management and Economics Innovations 03, no. 05 (2021): 46–52. http://dx.doi.org/10.37547/tajmei/volume03issue05-08.

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The article considers a method for constructing correlation models for finite-type functions using a set of variables. The use of the method of unknown squares in the construction of correlation models and the construction of higher-quality models is also justified. The proposed correlation models are considered on the example of statistical data of the Bukhara region of the Republic of Uzbekistan.

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16

Moncrieff, D., and S. Wilson. "Finite basis set versus finite difference and finite element methods." Chemical Physics Letters 209, no. 4 (1993): 423–26. http://dx.doi.org/10.1016/0009-2614(93)80041-m.

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17

Biringen, S., and A. Saati. "Comparison of several finite-difference methods." Journal of Aircraft 27, no. 1 (1990): 90–92. http://dx.doi.org/10.2514/3.45900.

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18

Triana, Juan, and Luis Ferro. "Finite difference methods in image processing." Selecciones Matemáticas 8, no. 02 (2021): 411–16. http://dx.doi.org/10.17268/sel.mat.2021.02.17.

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19

Boutayeb, A., and E. H. Twizell. "Finite-difference methods for twelfth-order." Journal of Computational and Applied Mathematics 35, no. 1-3 (1991): 133–38. http://dx.doi.org/10.1016/0377-0427(91)90202-u.

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20

Lipnikov, Konstantin, Mikhail Shashkov, and Ivan Yotov. "Local flux mimetic finite difference methods." Numerische Mathematik 112, no. 1 (2008): 115–52. http://dx.doi.org/10.1007/s00211-008-0203-5.

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21

Junk, Michael, and Zhaoxia Yang. "Asymptotic analysis of finite difference methods." Applied Mathematics and Computation 158, no. 1 (2004): 267–301. http://dx.doi.org/10.1016/j.amc.2003.08.097.

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22

Sara, Raiat, and Ghorbani Ali. "Numerical Modeling of the Effects of a Group of Micropiles in Liquefiable Soils." Journal of Civil Engineering and Materials Application 7, no. 1 (2023): 33–42. https://doi.org/10.22034/jcema.2023.171495.

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As micropiles, small-diameter (d < 300 mm) piles installed in problematic liquefiable soils, are widely used in seismic areas, studying their behavior during an earthquake is of great importance. To validate the numerical modeling accurately, this study used the finite difference method to investigate the liquefaction phenomenon with the help of the FLAC3D (Fast Lagrangian Analysis of Continua in 3 Dimensions) Software and compared the results with those of Test No. 1 of the VELACS international project. Next, to check the efficiency of micropiles in liquefiable soils, such influential para

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23

Dao, Tuan Anh, Ken Mattsson, and Murtazo Nazarov. "Energy stable and accurate coupling of finite element methods and finite difference methods." Journal of Computational Physics 449 (January 2022): 110791. http://dx.doi.org/10.1016/j.jcp.2021.110791.

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24

Ibrahim, I. O., and S. Markus. "ON SHOOTING AND FINITE DIFFERENCE METHODS FOR NON-LINEAR TWO POINT BOUNDARY VALUE PROBLEMS." International Journal of Research - Granthaalayah 6, no. 1 (2018): 23–35. https://doi.org/10.5281/zenodo.1162064.

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The paper investigates the efficacy of non-linear two point boundary value problems via shooting and finite difference methods. It was observed that the shooting method provides better result as when compared to the finite difference methods with dirichlet boundary conditions. It was observed that the accuracy of the shooting method is dependent upon the integrator adopted.

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25

FAURE, S., D. PHAM, and R. TEMAM. "COMPARISON OF FINITE VOLUME AND FINITE DIFFERENCE METHODS AND APPLICATION." Analysis and Applications 04, no. 02 (2006): 163–208. http://dx.doi.org/10.1142/s0219530506000723.

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In this article, we consider finite volume methods based on a non-uniform grid. Finite volume methods are compared to finite difference methods based on a related grid. As an application, various convergence results are proved for the finite volume function spaces and for some model elliptic and parabolic boundary value problems using these discretization spaces.

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26

Ramos, J. I., and N. S. Winowich. "Finite difference and finite element methods for mhd channel flows." International Journal for Numerical Methods in Fluids 11, no. 6 (1990): 907–34. http://dx.doi.org/10.1002/fld.1650110614.

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27

LI, CHANGPIN, and FANHAI ZENG. "FINITE DIFFERENCE METHODS FOR FRACTIONAL DIFFERENTIAL EQUATIONS." International Journal of Bifurcation and Chaos 22, no. 04 (2012): 1230014. http://dx.doi.org/10.1142/s0218127412300145.

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In this review paper, the finite difference methods (FDMs) for the fractional differential equations are displayed. The considered equations mainly include the fractional kinetic equations of diffusion or dispersion with time, space and time-space derivatives. In some way, these numerical methods have similar form as the case for classical equations, some of which can be seen as the generalizations of the FDMs for the typical differential equations. And the classical tools, such as the von Neumann analysis method, the energy method and the Fourier method are extended to numerical methods for f

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28

Weideman, J. A. C., and B. M. Herbst. "Finite difference methods for an AKNS eigenproblem." Mathematics and Computers in Simulation 43, no. 1 (1997): 77–88. http://dx.doi.org/10.1016/s0378-4754(96)00057-2.

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29

Killingbeck, J. P., and A. Lakhlifi. "A perturbation approach to finite difference methods." Journal of Mathematical Chemistry 48, no. 4 (2010): 1036–43. http://dx.doi.org/10.1007/s10910-010-9723-1.

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30

Buratti, Marco, and Anamari Nakić. "Designs over finite fields by difference methods." Finite Fields and Their Applications 57 (May 2019): 128–38. http://dx.doi.org/10.1016/j.ffa.2019.02.006.

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31

Wong, Felix S. "Finite element/difference methods in random vibration." Computers & Structures 23, no. 1 (1986): 77–85. http://dx.doi.org/10.1016/0045-7949(86)90109-4.

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32

Vollebregt, Edwin. "Abstract Level Parallelization of Finite Difference Methods." Scientific Programming 6, no. 4 (1997): 331–44. http://dx.doi.org/10.1155/1997/321965.

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A formalism is proposed for describing finite difference calculations in an abstract way. The formalism consists of index sets and stencils, for characterizing the structure of sets of data items and interactions between data items (“neighbouring relations”). The formalism provides a means for lifting programming to a more abstract level. This simplifies the tasks of performance analysis and verification of correctness, and opens the way for automaticcode generation. The notation is particularly useful in parallelization, for the systematic construction of parallel programs in a process/channe

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33

Bazan, C., M. Abouali, J. Castillo, and P. Blomgren. "Mimetic finite difference methods in image processing." Computational & Applied Mathematics 30, no. 3 (2011): 701–20. http://dx.doi.org/10.1590/s1807-03022011000300012.

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34

Yao, Gang, Nuno Vieira da Silva, Henry Alexander Debens, and Di Wu. "Accurate seabed modeling using finite difference methods." Computational Geosciences 22, no. 2 (2017): 469–84. http://dx.doi.org/10.1007/s10596-017-9705-5.

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35

Towers, John D. "Finite difference methods for approximating Heaviside functions." Journal of Computational Physics 228, no. 9 (2009): 3478–89. http://dx.doi.org/10.1016/j.jcp.2009.01.026.

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36

Mastin, C. Wayne. "Implicit finite difference methods on composite grids." Journal of Computational and Applied Mathematics 20 (November 1987): 317–23. http://dx.doi.org/10.1016/0377-0427(87)90148-8.

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37

Su, Lijuan, Wenqia Wang, and Qiuyan Xu. "Finite difference methods for fractional dispersion equations." Applied Mathematics and Computation 216, no. 11 (2010): 3329–34. http://dx.doi.org/10.1016/j.amc.2010.04.060.

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38

Ramos, J. I. "Adaptive finite difference methods for liquid membranes." International Journal for Numerical Methods in Engineering 34, no. 3 (1992): 823–36. http://dx.doi.org/10.1002/nme.1620340309.

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39

Strelkov, N. A. "Direct and inverse finite difference projection methods." Mathematical Notes 57, no. 4 (1995): 407–13. http://dx.doi.org/10.1007/bf02304169.

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40

Beillard, B., J. Andrieu, and B. Jecko. "Coupling of methods: finite difference time domain and asymptotic methods." Electronics Letters 32, no. 4 (1996): 308. http://dx.doi.org/10.1049/el:19960213.

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41

Duru, H., B. Gürbüz, and A. B. Chiyaneh. "A second-order finite difference method for singularly perturbed nonlinear delay parabolic problems with periodic initial-boundary conditions." Mechanics and Technologies, no. 3 (September 30, 2024): 447–51. http://dx.doi.org/10.55956/gxlz1174.

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In this paper, a numerical study for the singularly perturbed nonlinear delay parabolic problems with boundary conditions are made. A finite difference method based on the mesh with adaptive points are proposed. The method employs interpolating quadrature rules containing integral remainder terms with linear basis functions ensuring a second-order accuracy rate on an adaptive mesh. The proposed method exhibits second-order convergence in the space variable, and first-order in the time variable, regardless of the perturbation parameter. Stability analysis is provided, and numerical experiments

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42

Chan, K. H., Ligang Li, and Xinhao Liao. "Modelling the core convection using finite element and finite difference methods." Physics of the Earth and Planetary Interiors 157, no. 1-2 (2006): 124–38. http://dx.doi.org/10.1016/j.pepi.2006.03.014.

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43

Steppat, Michael. "Modeling of steeldrum sounds using finite element and finite difference methods." Journal of the Acoustical Society of America 119, no. 5 (2006): 3324. http://dx.doi.org/10.1121/1.4786361.

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44

Lugo Jiménez, Abdul Abner, Guelvis Enrique Mata Díaz, and Bladismir Ruiz. "A comparative analysis of methods: mimetics, finite differences and finite elements for 1-dimensional stationary problems." Selecciones Matemáticas 8, no. 1 (2021): 1–11. http://dx.doi.org/10.17268/sel.mat.2021.01.01.

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Numerical methods are useful for solving differential equations that model physical problems, for example, heat transfer, fluid dynamics, wave propagation, among others; especially when these cannot be solved by means of exact analysis techniques, since such problems present complex geometries, boundary or initial conditions, or involve non-linear differential equations. Currently, the number of problems that are modeled with partial differential equations are diverse and these must be addressed numerically, so that the results obtained are more in line with reality. In this work, a comparison

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45

Jeon, Youngmok, Eun-Jae Park, and Dong-wook Shin. "Hybrid Spectral Difference Methods for an Elliptic Equation." Computational Methods in Applied Mathematics 17, no. 2 (2017): 253–67. http://dx.doi.org/10.1515/cmam-2016-0043.

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AbstractA locally conservative, hybrid spectral difference method (HSD) is presented and analyzed for the Poisson equation. The HSD is composed of two types of finite difference approximations; the cell finite difference and the interface finite difference. Embedded static condensation on cell interior unknowns considerably reduces the global couplings, resulting in the system of equations in the cell interface unknowns only. A complete ellipticity analysis is provided. The optimal order of convergence in the semi-discrete energy norms is proved. Several numerical results are given to show the

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46

Adil, Kadyrov, Amanbayev Sabit, Ganyukov Aleksandr, Balabekova Kyrmyzy, and Kurmasheva Bahyt. "Solving Traffic Congestion Problems and Definition Stress-Strain State of Curvilinear Overpass Module Sector-Ring Slab." International Journal of Engineering and Advanced Technology (IJEAT) 9, no. 3 (2020): 44–48. https://doi.org/10.35940/ijeat.A1236.029320.

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In the article we discuss the construction of curvilinear overpass module sector – ring slab. Calculation of constructive elements and studied the stress-strain state of a sector-ring. The purpose is the development of the technique and calculation for the new construction of a curvilinear overpass for reduction of traffic jams. The methods uses are mathematical analysis, method of finite elements, method of finite differences, and analytical method of relocation. The purpose of the study is calculate constructive elements of module sector – ring slab and decrease of traffic jams.

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47

Shiv, Narain*1 &. Meenu Goel2. "AN IMPLICIT NUMERICAL SCHEME FOR FRACTIONAL ADVENTION DIFFUSION EQUATION." GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES 6, no. 5 (2019): 94–99. https://doi.org/10.5281/zenodo.2694021.

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In this paper, a finite difference scheme is presented for time fractional advection diffusion equation (TFADE). This equation is derived from classical advection diffusion equation with variable coefficients on replacing classical integer order derivatives by their fractional counterpart. An advection diffusion equation describes physical phenomenon where particle, energy or other physical quantities are transferred inside a physical system due to combined effect of advection and diffusion. To address anomalous diffusion like sub diffusion or super diffusion, classical integer derivatives are

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48

Faraj, Bawar Mohammed, and Ali Akgul. "DIFFERENCE SCHEME METHOD FOR THE NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS." Transactions in Mathematical and Computational Sciences 1, no. 2 (2022): 12–22. https://doi.org/10.5281/zenodo.5816159.

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In this study, wave equations with initial boundary conditions have been studied. The general form of the wave equation has been derived. The first order and second order difference schemes were established for the presented IBVP. The stability of the difference schemes has been guaranteed. The approximation solution of the problem was achieved by using finite difference methods. Two different examples are provided. A comparison between the exact and approximation solution has been carried out. Absolute errors of the problem have been presented by using MATLAB software. Moreover, the compariso

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49

Al-Bayati, Abbas, Saad Manaa, and Ekhlass Al-Rawi. "The Finite Difference Methods for Hyperbolic – Parabolic Equations." AL-Rafidain Journal of Computer Sciences and Mathematics 2, no. 2 (2005): 57–71. http://dx.doi.org/10.33899/csmj.2005.164084.

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50

Ndayisenga, Serge, Leonid A. Sevastianov, and Konstantin P. Lovetskiy. "Finite-difference methods for solving 1D Poisson problem." Discrete and Continuous Models and Applied Computational Science 30, no. 1 (2022): 62–78. http://dx.doi.org/10.22363/2658-4670-2022-30-1-62-78.

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The paper discusses the formulation and analysis of methods for solving the one-dimensional Poisson equation based on finite-difference approximations - an important and very useful tool for the numerical study of differential equations. In fact, this is a classical approximation method based on the expansion of the solution in a Taylor series, based on which the recent progress of theoretical and practical studies allowed increasing the accuracy, stability, and convergence of methods for solving differential equations. Some of the features of this analysis include interesting extensions to cl

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