二阶精度混合Legendre-球面调和拟谱方法求解Fisher 型方程

doi:10.3969/j.issn.1007-2861.2014.01.038

上海大学学报(自然科学版) ›› 2015, Vol. 21 ›› Issue (03): 331-335.doi: 10.3969/j.issn.1007-2861.2014.01.038

二阶精度混合Legendre-球面调和拟谱方法求解Fisher 型方程

邓红梅, 黄伟

上海大学理学院, 上海200444

收稿日期:2013-12-16 出版日期:2015-06-22 发布日期:2015-06-22
通讯作者: 黄伟(1960—), 男, 副教授, 研究方向为偏微分方程的谱方法. E-mail: weihuang@mail.shu.edu.cn
作者简介:黄伟(1960—), 男, 副教授, 研究方向为偏微分方程的谱方法. E-mail: weihuang@mail.shu.edu.cn
基金资助:
国家自然科学基金资助项目(11372170,11176015); 上海市重点学科建设资助项目(J50101)

A second order accurate mixed legendre-spherical harmonic pseudo-spectral method for the
Fisher equation

DENG Hong-mei, HUANG Wei

Received:2013-12-16 Online:2015-06-22 Published:2015-06-22

摘要/Abstract

摘要： 提出了求解两同心球所介区域上Fisher 型方程的时间方向二阶精度的混合Legendre-球面调和拟谱格式. 该格式在半径方向选择Gauss 型的Legendre 插值逼近, 球面方向选择球面调和插值逼近, 而时间方向的导数采用二阶中心差商离散. 数值结果显示, 该算法具有较好的稳定性和较高精度.

关键词: Fisher型方程, Legendre-球面调和拟谱方法, 两同心球所介区域, 时间方向二阶精度

Abstract: The paper proposes a second mixed Legendre-spherical harmonic pseudospectral scheme for the Fisher equation in a domain between two concentric balls. Legendre interpolation is used in the radial direction, and spherical harmonic interpolation in other directions. The second order central difference quotient is used for time derivatives. Numerical results show high accuracy of the proposed algorithm.

Key words: domain between two concentric balls, Fisher equation, mixed Legendre-spherical harmonic spectral method, second order accurate in the temporal direction

中图分类号:

O 241.82

邓红梅, 黄伟. 二阶精度混合Legendre-球面调和拟谱方法求解Fisher 型方程[J]. 上海大学学报(自然科学版), 2015, 21(03): 331-335.

DENG Hong-Mei, HUANG Wei. A second order accurate mixed legendre-spherical harmonic pseudo-spectral method for the
Fisher equation[J]. Journal of Shanghai University（Natural Science Edition）, 2015, 21(03): 331-335.

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二阶精度混合Legendre-球面调和拟谱方法求解Fisher 型方程

A second order accurate mixed legendre-spherical harmonic pseudo-spectral method for the
Fisher equation

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二阶精度混合Legendre-球面调和拟谱方法求解Fisher 型方程

A second order accurate mixed legendre-spherical harmonic pseudo-spectral method for the Fisher equation

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A second order accurate mixed legendre-spherical harmonic pseudo-spectral method for the
Fisher equation