A three level linearized compact difference scheme for a fourth-order reaction-diffusion equation

被引：2

作者：

Boujlida, Hanen ^{[1
]}

Ismail, Kaouther ^{[2
]}

Omrani, Khaled ^{[3
]}

机构：

[1] Univ Sousse, Ecole Super Sci & Technol Hammam Sousse, LAMMDA, 4011 H Sousse,Rue L Abassi, Sousse, Tunisia

[2] Univ Carthage, Ecole Polytech Tunis, Phys Math Modelisat Quant & Concept Mecan, LR18ES45, Rue Khawarezmi, La Marsa 2078, Tunisia

[3] Univ Tunis Manar, Inst Preparatoire Etud Ingenieurs El Manar, Phys Math Modelisat Quant & Concept Mecan, LR18ES45, Tunis 2092, Tunisia

来源：

APPLIED NUMERICAL MATHEMATICS | 2024年 / 195卷

关键词：

EFK equation; Linearized compact difference scheme; Solvability; Convergence; COLLOCATION METHOD; ERROR ANALYSIS; KOLMOGOROV;

D O I：

10.1016/j.apnum.2023.09.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A high-order accuracy finite difference scheme is investigated to solve the one-dimensional extended Fisher-Kolmogorov (EFK) equation. A three level linearized compact finite difference scheme is proposed. Priori estimates and unique solvability are discussed in detail by the discrete energy method. The unconditional stability and convergence of the difference solution are proved. The new compact difference scheme has secondorder accuracy in time and fourth-order accuracy in space in maximum norm. Numerical experiments demonstrate the accuracy, efficiency of our proposed technique. (c) 2023 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：126 / 141

页数：16

共 33 条

[1] A reduced-order variational multiscale interpolating element free Galerkin technique based on proper orthogonal decomposition for solving Navier-Stokes equations coupled with a heat transfer equation: Nonstationary incompressible Boussinesq equations
Abbaszadeh, Mostafa
Dehghan, Mehdi
Khodadadian, Amirreza
Noii, Nima
Heitzinger, Clemens
Wick, Thomas
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2021, 426
[2] Legendre spectral element method (LSEM) to simulate the two-dimensional system of nonlinear stochastic advection-reaction-diffusion models
Abbaszadeh, Mostafa
Dehghan, Mehdi
Khodadadian, Amirreza
Wick, Thomas
[J]. APPLICABLE ANALYSIS, 2022, 101 (06) : 2279 - 2294
[3] Error analysis of interpolating element free Galerkin method to solve non-linear extended Fisher-Kolmogorov equation
Abbaszadeh, Mostafa
Dehghan, Mehdi
Khodadadian, Amirreza
Heitzinger, Clemens
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2020, 80 (01) : 247 - 262
[4] Investigation of the Oldroyd model as a generalized incompressible Navier-Stokes equation via the interpolating stabilized element free Galerkin technique
Abbaszadeh, Mostafa
Dehghan, Mehdi
[J]. APPLIED NUMERICAL MATHEMATICS, 2020, 150 : 274 - 294
[5] A direct meshless local collocation method for solving stochastic Cahn-Hilliard-Cook and stochastic Swift-Hohenberg equations
Abbaszadeh, Mostafa
Khodadadian, Amirreza
Parvizi, Maryam
Dehghan, Mehdi
Heitzinger, Clemens
[J]. ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2019, 98 : 253 - 264
[6] MULTIDIMENSIONAL NON-LINEAR DIFFUSION ARISING IN POPULATION-GENETICS
ARONSON, DG
WEINBERGER, HF
[J]. ADVANCES IN MATHEMATICS, 1978, 30 (01) : 33 - 76
[7] Gegenbauer wavelet collocation method for the extended Fisher-Kolmogorov equation in two dimensions
Celik, Ibrahim
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (08) : 5615 - 5628
[8] NATURE OF SPATIAL CHAOS
COULLET, P
ELPHICK, C
REPAUX, D
[J]. PHYSICAL REVIEW LETTERS, 1987, 58 (05) : 431 - 434
[9] Orthogonal cubic spline collocation method for the extended Fisher-Kolmogorov equation
Danumjaya, P
Pani, AK
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 174 (01) : 101 - 117
[10] Mixed finite element methods for a fourth order reaction diffusion equation
Danumjaya, P.
Pani, Amiya K.
[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2012, 28 (04) : 1227 - 1251

← 1 2 3 4 →