A NOVEL SPECTRAL APPROXIMATION FOR THE TWO-DIMENSIONAL FRACTIONAL SUB-DIFFUSION PROBLEMS

被引：0

作者：

Bhrawy, A. H. ^{[1
,2
]}

Zaky, M. A. ^{[3
]}

Baleanu, D. ^{[4
,5
]}

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

机构：

[1] King Abdulaziz Univ, Fac Sci, Dept Math, Jeddah, Saudi Arabia

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

[3] Natl Res Ctr, Dept Appl Math, Cairo, Egypt

[4] Cankaya Univ, Fac Art & Sci, Dept Math & Comp Sci, Ankara, Turkey

[5] Inst Space Sci, RO-077125 Magurele, Romania

来源：

ROMANIAN JOURNAL OF PHYSICS | 2015年 / 60卷 / 3-4期

关键词：

Two-dimensional fractional diffusion equations; Tau method; Shifted Jacobi polynomials; Operational matrix; Caputo derivative; IMPLICIT NUMERICAL-METHOD; COLLOCATION METHOD; DIFFERENCE SCHEME; EQUATIONS; STABILITY;

D O I：

暂无

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

This paper reports a new numerical method that enables easy and convenient discretization of a two-dimensional sub-diffusion equation with fractional derivatives of any order. The suggested method is based on Jacobi tau spectral procedure together with the Jacobi operational matrix for fractional derivatives, described in the Caputo sense. Such approach has the advantage of reducing the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. The validity and effectiveness of the method are demonstrated by solving two numerical examples, which are presented in the form of tables and graphs to make more easier comparisons with the exact solutions and the results obtained by other methods.

引用

页码：344 / 359

页数：16

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