First-order and second-order, chaos-free, finite difference schemes for Fisher equation

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	First-order and second-order, chaos-free, finite difference schemes for Fisher equation
	Sun, G ; Wu, HM ; Wang, LE
	2001-09-01
发表期刊	JOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN	0254-9409
卷号	19 期号:5 页码:519-530
摘要	A new class of finite difference schemes is constructed for Fisher partial differential equation i.e. the reaction-diffusion equation with stiff source term: alphau(1 - u). These schemes have the properties that they reduce to high fidelity algorithms in the diffusion-free case namely in which the numerical solutions preserve the properties inherent in the exact solutions for arbitrary time step-size and reaction coefficient alpha > 0, and all nonphysical spurious solutions including bifurcations and chaos that normally appear in the standard discrete models of Fisher partial differential equation will not occur. The implicit schemes so developed obtain the numerical solutions by solving a single linear algebraic system at each step. The boundness and asymptotic behaviour of numerical solutions obtained by all these schemes are given. The approach constructing the above schemes can be extended to react ion-diffusion equations with other stiff source terms.
关键词	reaction-diffusion equation fidelity algorithm
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000170843600008
出版者	VSP BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/16792
专题	中国科学院数学与系统科学研究院
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100080, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Sun, G,Wu, HM,Wang, LE. First-order and second-order, chaos-free, finite difference schemes for Fisher equation[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2001,19(5):519-530.
APA	Sun, G,Wu, HM,&Wang, LE.(2001).First-order and second-order, chaos-free, finite difference schemes for Fisher equation.JOURNAL OF COMPUTATIONAL MATHEMATICS,19(5),519-530.
MLA	Sun, G,et al."First-order and second-order, chaos-free, finite difference schemes for Fisher equation".JOURNAL OF COMPUTATIONAL MATHEMATICS 19.5(2001):519-530.