A front-fixing numerical method for a free boundary nonlinear diffusion logistic population model

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• 作者：M.-A. Piqueras ^{mipigar@cam.upv.es" class="auth_mail" title="E-mail the corresponding author} ; R. Company ; ^{rcompany@imm.upv.es" class="auth_mail" title="E-mail the corresponding author} ; L. Jó ; dar ^{ljodar@imm.upv.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Diffusive logistic population model ; Moving boundary ; Stefan condition ; Finite difference ; Numerical analysis ; Computing simulation
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：309
• 期：Complete
• 页码：473-481
• 全文大小：579 K

文摘

The spatial–temporal spreading of a new invasive species in a habitat has interest in ecology and is modeled by a moving boundary diffusion logistic partial differential problem, where the moving boundary represents the unknown expanding front of the species. In this paper a front-fixing approach is applied in order to transform the original moving boundary problem into a fixed boundary one. A finite difference method preserving qualitative properties of the theoretical solution is proposed. Results are illustrated with numerical experiments.