Highly accurate technique for solving distributed-order time-fractional-sub-diffusion equations of fourth order

被引：11

作者：

Abdelkawy, M. A. ^{[1
,2
]}

Babatin, Mohammed M. ^{[1
]}

Lopes, Antonio M. ^{[3
]}

机构：

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

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

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

来源：

COMPUTATIONAL & APPLIED MATHEMATICS | 2020年 / 39卷 / 02期

关键词：

Spectral collocation method; Gauss-Lobatto quadrature; Caputo fractional derivative; Distributed order time-fractional diffusion-wave equation; FINITE-DIFFERENCE METHODS; OPERATIONAL MATRIX; NUMERICAL-SOLUTION; COLLOCATION METHOD; CONVERGENCE ANALYSIS; ANOMALOUS DIFFUSION; GAUSS-COLLOCATION; SPATIAL ACCURACY; BOUNDED DOMAIN; ELEMENT-METHOD;

D O I：

10.1007/s40314-020-1070-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents a new method for calculating the numerical solution of distributed-order time-fractional-sub-diffusion equations (DO-TFSDE) of fourth order. The method extends the shifted fractional Jacobi (SFJ) collocation scheme for discretizing both the time and space variables. The approximate solution is expressed as a finite expansion of SFJ polynomials whose derivatives are evaluated at the SFJ quadrature points. The process yields a system of algebraic equations that are solved analytically. The new method is compared with alternative numerical algorithms when solving different types of DO-TFSDE. The results show that the proposed method exhibits superior accuracy with an exponential convergence rate.

引用

页数：22

共 56 条

[1] Shifted fractional Jacobi spectral algorithm for solving distributed order time-fractional reaction-diffusion equations [J].