Numerical solution of variable-order fractional integro-partial differential equations via Sinc collocation method based on single and double exponential transformations

被引：56

作者：

Babaei, A. ^{[1
]}

Moghaddam, B. P. ^{[2
]}

Banihashemi, S. ^{[1
]}

Machado, J. A. T. ^{[3
]}

机构：

[1] Univ Mazandaran, Dept Math, Babol Sar, Iran

[2] Islamic Azad Univ, Dept Math, Lahijan Branch, Lahijan, Iran

[3] Inst Engn Porto, Dept Elect Engn, Porto, Portugal

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2020年 / 82卷 / 82期

关键词：

Variable-order fractional calculus; Integro-partial differential equations; Diffusion equation; Sinc function; Numerical analysis; Spline approximation; Convergence and error; PARTIAL INTEGRODIFFERENTIAL EQUATION; SCHEME; APPROXIMATIONS;

D O I：

10.1016/j.cnsns.2019.104985

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper addresses the numerical solution of the multi-dimensional variable-order fractional integro-partial differential equations. The upwind scheme and a piecewise linear interpolation, are proposed to approximate the Coimbra variable-order fractional derivatives and integral term with kernel, respectively. Two new approaches via the Sinc collocation method based on single and double exponential transformations are adopted for the temporal and spatial discretizations, respectively. The convergence behaviour of the methods is analysed and the error bounds are provided. In addition, four test problems illustrate the validity and effectiveness of the proposed algorithms. (C) 2019 Elsevier B.V. All rights reserved.

引用

页数：21

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