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Volume 6, Issue 4
A Fully Discrete Spectral Method for Fisher’s Equation on the Whole Line

Yu-Jian Jiao, Tian-Jun Wang & Qiong Zhang

DOI: 10.4208/eajam.310315.120716a

East Asian J. Appl. Math., 6 (2016), pp. 400-415.

Published online: 2018-02

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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 equation, spectral method, generalised Hermite function, problem on the whole line.

  • AMS Subject Headings

34A34, 34B40, 41A30, 65L60, 65M70

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-6-400, author = {Yu-Jian Jiao, Tian-Jun Wang and Qiong Zhang}, title = {A Fully Discrete Spectral Method for Fisher’s Equation on the Whole Line}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {6}, number = {4}, pages = {400--415}, 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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.310315.120716a}, url = {http://global-sci.org/intro/article_detail/eajam/10808.html} }
TY - JOUR T1 - A Fully Discrete Spectral Method for Fisher’s Equation on the Whole Line AU - Yu-Jian Jiao, Tian-Jun Wang & Qiong Zhang JO - East Asian Journal on Applied Mathematics VL - 4 SP - 400 EP - 415 PY - 2018 DA - 2018/02 SN - 6 DO - http://doi.org/10.4208/eajam.310315.120716a UR - https://global-sci.org/intro/article_detail/eajam/10808.html KW - Fisher’s equation, spectral method, generalised Hermite function, problem on the whole line. AB -

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.

Yu-Jian Jiao, Tian-Jun Wang and Qiong Zhang. (2018). A Fully Discrete Spectral Method for Fisher’s Equation on the Whole Line. East Asian Journal on Applied Mathematics. 6 (4). 400-415. doi:10.4208/eajam.310315.120716a
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