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A Fully Discrete Spectral Method for Fisher’s Equation on the Whole Line

Part of: General theory in ordinary differential equations Partial differential equations, initial value and time-dependent initial-boundary value problems Boundary value problems Approximations and expansions Numerical analysis: Ordinary differential equations

Published online by Cambridge University Press:  19 October 2016

Yu-Jian Jiao ,
Tian-Jun Wang  and
Qiong Zhang
Yu-Jian Jiao
Affiliation:
Department of Mathematics, Shanghai Normal University, Shanghai, 200234, P. R. China; Scientific Computing Key Laboratory of Shanghai Universities
Tian-Jun Wang*
Affiliation:
Henan University of Science and Technology, Luoyang, 471003, P. R. China
Qiong Zhang
Affiliation:
Henan University of Science and Technology, Luoyang, 471003, P. R. China
*
*Corresponding author. Email address:wangtianjun64@163.com (T.-J. Wang)
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Abstract

A generalised Hermite spectral method for Fisher's equation in genetics with different asymptotic solution behaviour at infinities is proposed, involving a fully discrete scheme using a second order finite difference approximation in the time. The convergence and stability of the scheme are analysed, and some numerical results demonstrate its efficiency and substantiate our theoretical analysis.

Keywords

Fisher's equationspectral methodgeneralised Hermite functionproblem on the whole line

MSC classification

Secondary: 34A34: Nonlinear equations and systems, general 34B40: Boundary value problems on infinite intervals 41A30: Approximation by other special function classes 65L60: Finite elements, Rayleigh-Ritz, Galerkin and collocation methods 65M70: Spectral, collocation and related methods
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 6 , Issue 4 , November 2016 , pp. 400 - 415
Copyright
Copyright © Global-Science Press 2016 

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