A numerical study by using the Chebyshev collocation method for a problem of biological invasion: Fractional Fisher equation

被引：43

作者：

Khader, Mohamed M. ^{[1
,2
]}

Saad, Khaled M. ^{[3
,4
]}

机构：

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

[2] Benha Univ, Dept Math, Fac Sci, Banha, Egypt

[3] Najran Univ, Dept Math, Coll Arts & Sci, Najran, Saudi Arabia

[4] Taiz Univ, Dept Math, Fac Appl Sci, Taizi, Yemen

来源：

INTERNATIONAL JOURNAL OF BIOMATHEMATICS | 2018年 / 11卷 / 08期

关键词：

Fractional Fisher equation; FDM; Chebyshev polynomials; convergence analysis; WAVE; DERIVATIVES;

D O I：

10.1142/S1793524518500997

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In this paper, an efficient numerical method is introduced for solving the fractional (Caputo sense) Fisher equation. We use the spectral collocation method which is based upon Chebyshev approximations. The properties of Chebyshev polynomials of the third kind are used to reduce the proposed problem to a system of ODEs, which is solved by the finite difference method (FDM). Some theorems about the convergence analysis are stated and proved. A numerical simulation is given and the results are compared with the exact solution.

引用

页数：15

共 31 条

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[3]

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[4]

[Anonymous], 1999, FRACTIONAL DIFFERENT

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