A space-time spectral approximation for solving nonlinear variable-order fractional sine and Klein-Gordon differential equations

被引：14

作者：

Doha, E. H. ^{[1
]}

Abdelkawy, M. A. ^{[2
,3
]}

Amin, A. Z. M. ^{[4
]}

Lopes, Antonio M. ^{[5
]}

机构：

[1] Cairo Univ, Fac Sci, Dept Math, Giza, Egypt

[2] Al Imam Mohammad Ibn Saud Islamic Univ IMSIU, Coll Sci, Dept Math & Stat, Riyadh, Saudi Arabia

[3] Beni Suef Univ, Fac Sci, Dept Math, Bani Suwayf, Egypt

[4] CIC, Inst Engn, Dept Basic Sci, Giza, Egypt

[5] Univ Porto, Fac Engn, INEGI, UISPA,LAETA, Porto, Portugal

来源：

COMPUTATIONAL & APPLIED MATHEMATICS | 2018年 / 37卷 / 05期

关键词：

Fractional calculus; Caputo fractional derivative of variable order; Fractional sine and Klein-Gordon differential equation; Spectral collocation method; 65M70; 65N35; 26A33; 35R11; COLLOCATION METHOD; DIFFUSION EQUATION; NUMERICAL-ANALYSIS; CONVERGENCE; ALGORITHM; TRANSPORT; SCHEME;

D O I：

10.1007/s40314-018-0695-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we propose an efficient spectral numerical method for solving sine and Klein-Gordon nonlinear variable-order fractional differential equations with the initial and Dirichlet boundary conditions. The approach is based on the shifted Legendre-Gauss and Chebyshev-Gauss collocation methods. The Caputo fractional derivative of variable order is adopted, and the original problems are reduced to systems of algebraic equations. The validity and effectiveness of the method is demonstrated by means of several numerical examples.

引用

页码：6212 / 6229

页数：18

共 46 条

[41] A compact difference scheme for a two dimensional fractional Klein-Gordon equation with Neumann boundary conditions
Vong, Seakweng
Wang, Zhibo
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2014, 274 : 268 - 282
[42] A NEW FRACTIONAL DERIVATIVE WITHOUT SINGULAR KERNEL Application to the Modelling of the Steady Heat Flow
Yang, Xiao-Jun
Srivastava, Hari M.
Machado, J. A. Tenreiro
[J]. THERMAL SCIENCE, 2016, 20 (02): : 753 - 756
[43] A new numerical technique for solving the local fractional diffusion equation: Two-dimensional extended differential transform approach
Yang, Xiao-Jun
Tenreiro Machado, J. A.
Srivastava, H. M.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2016, 274 : 143 - 151
[44] Nonlinear dynamics for local fractional Burgers' equation arising in fractal flow
Yang, Xiao-Jun
Machado, J. A. Tenreiro
Hristov, Jordan
[J]. NONLINEAR DYNAMICS, 2016, 84 (01) : 3 - 7
[45] Numerical analysis of a new space-time variable fractional order advection-dispersion equation
Zhang, H.
Liu, F.
Zhuang, P.
Turner, I.
Anh, V.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2014, 242 : 541 - 550
[46] Second-order approximations for variable order fractional derivatives: Algorithms and applications
Zhao, Xuan
Sun, Zhi-zhong
Karniadakis, George Em
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 293 : 184 - 200

← 1 2 3 4 5 →