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

[1] Space-Time Spectral Collocation Algorithm for the Variable-Order Galilei Invariant Advection Diffusion Equations with a Nonlinear Source Term [J].