A NUMERICAL METHOD FOR TWO-DIMENSIONAL DISTRIBUTED-ORDER FRACTIONAL NONLINEAR SOBOLEV EQUATION

被引：0

作者：

Zhagharian, Sh. ^{[1
]}

Heydari, M. H. ^{[1
]}

Razzaghi, M. ^{[2
]}

机构：

[1] Shiraz Univ Technol, Dept Math, Modarres Blvd, Shiraz 7155713876, Iran

[2] Mississippi State Univ, Dept Math & Stat, Mississippi State, MS 39762 USA

来源：

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2023年 / 13卷 / 05期

关键词：

Distributed-order fractional derivative; nonlinear Sobolev equation; Chebyshev cardinal polynomials; operational matrices; SCHEME;

D O I：

10.11948/20220480

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This study introduces the distributed-order fractional version of the nonlinear two-dimensional Sobolev equation. The orthonormal Chebyshev cardinal polynomials are used to construct a numerical method for this equation. To this end, some derivative matrices related to these polynomials are obtained. The proposed approach turns to solve this equation into solving a nonlinear system of algebraic equations by approximating the unknown solution using the expressed polynomials and employing their derivative matrices. The applicability and validity of this method are examined by solving three examples.

引用

页码：2630 / 2645

页数：16

共 31 条

[1] Error estimate of second-order finite difference scheme for solving the Riesz space distributed-order diffusion equation
Abbaszadeh, Mostafa
[J]. APPLIED MATHEMATICS LETTERS, 2019, 88 : 179 - 185
[2] A generalized model for the uniaxial isothermal deformation of a viscoelastic body
Atanackovic, TM
[J]. ACTA MECHANICA, 2002, 159 (1-4) : 77 - 86
[3] SARS-CoV-2 rate of spread in and across tissue, groundwater and soil: A meshless algorithm for the fractional diffusion equation
Bavi, O.
Hosseininia, M.
Heydari, M. H.
Bavi, N.
[J]. ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2022, 138 : 108 - 117
[4] Canuto C, 1988, SPECTRAL METHODS FLU
[5] A numerical method for finding solution of the distributed-order time-fractional forced Korteweg-de Vries equation including the Caputo fractional derivative
Derakhshan, Mohammad Hossein
Aminataei, Azim
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2022, 45 (05) : 3144 - 3165
[6] NUMERICAL-SOLUTION OF SOBOLEV PARTIAL-DIFFERENTIAL EQUATIONS
EWING, RE
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1975, 12 (03) : 345 - 363
[7] Approximate solution of two-dimensional Sobolev equation using a mixed Lucas and Fibonacci polynomials
Haq, Sirajul
Ali, Ihteram
[J]. ENGINEERING WITH COMPUTERS, 2022, 38 (SUPPL 3) : 2059 - 2068
[8] Piecewise Chebyshev cardinal functions: Application for constrained fractional optimal control problems
Heydari, M. H.
Razzaghi, M.
[J]. CHAOS SOLITONS & FRACTALS, 2021, 150
[9] Numerical treatment of the strongly coupled nonlinear fractal-fractional Schrodinger equations through the shifted Chebyshev cardinal functions
Heydari, M. H.
Atangana, A.
Avazzadeh, Z.
Yang, Y.
[J]. ALEXANDRIA ENGINEERING JOURNAL, 2020, 59 (04) : 2037 - 2052
[10] A cardinal approach for nonlinear variable-order time fractional Schrodinger equation defined by Atangana-Baleanu-Caputo derivative
Heydari, M. H.
Atangana, A.
[J]. CHAOS SOLITONS & FRACTALS, 2019, 128 : 339 - 348

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