KMS Of Academy of mathematics and systems sciences, CAS
First-order and second-order, chaos-free, finite difference schemes for Fisher equation | |
Sun, G; Wu, HM; Wang, LE | |
2001-09-01 | |
Source Publication | JOURNAL OF COMPUTATIONAL MATHEMATICS |
ISSN | 0254-9409 |
Volume | 19Issue:5Pages:519-530 |
Abstract | 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. |
Keyword | reaction-diffusion equation fidelity algorithm |
Language | 英语 |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000170843600008 |
Publisher | VSP BV |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/16792 |
Collection | 中国科学院数学与系统科学研究院 |
Affiliation | 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 |
Recommended Citation 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. |
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