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Volume 12, Issue 1
Numerical Investigations of a Class of Biological Models on Unbounded Domain

Qiumei Huang, Dongfang Li & Jiwei Zhang

DOI: 10.4208/nmtma.OA-2017-0117

Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 169-186.

Published online: 2018-09

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  • Abstract

This paper is concerned with numerical computations of a class of biological models on unbounded spatial domains. To overcome the unboundedness of spatial domain, we first construct efficient local absorbing boundary conditions (LABCs) to reformulate the Cauchy problem into an initial-boundary value (IBV) problem. After that, we construct a linearized finite difference scheme for the reduced IVB problem, and provide the corresponding error estimates and stability analysis. The delay-dependent dynamical properties on the Nicholson's blowflies equation and the Mackey-Glass equation are numerically investigated. Finally, numerical examples are given to demonstrate the efficiency of our LABCs and theoretical results of the numerical scheme.

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@Article{NMTMA-12-169, author = {Qiumei Huang, Dongfang Li and Jiwei Zhang}, title = {Numerical Investigations of a Class of Biological Models on Unbounded Domain}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {12}, number = {1}, pages = {169--186}, abstract = {

This paper is concerned with numerical computations of a class of biological models on unbounded spatial domains. To overcome the unboundedness of spatial domain, we first construct efficient local absorbing boundary conditions (LABCs) to reformulate the Cauchy problem into an initial-boundary value (IBV) problem. After that, we construct a linearized finite difference scheme for the reduced IVB problem, and provide the corresponding error estimates and stability analysis. The delay-dependent dynamical properties on the Nicholson's blowflies equation and the Mackey-Glass equation are numerically investigated. Finally, numerical examples are given to demonstrate the efficiency of our LABCs and theoretical results of the numerical scheme.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2017-0117}, url = {http://global-sci.org/intro/article_detail/nmtma/12696.html} }
TY - JOUR T1 - Numerical Investigations of a Class of Biological Models on Unbounded Domain AU - Qiumei Huang, Dongfang Li & Jiwei Zhang JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 169 EP - 186 PY - 2018 DA - 2018/09 SN - 12 DO - http://doi.org/10.4208/nmtma.OA-2017-0117 UR - https://global-sci.org/intro/article_detail/nmtma/12696.html KW - AB -

This paper is concerned with numerical computations of a class of biological models on unbounded spatial domains. To overcome the unboundedness of spatial domain, we first construct efficient local absorbing boundary conditions (LABCs) to reformulate the Cauchy problem into an initial-boundary value (IBV) problem. After that, we construct a linearized finite difference scheme for the reduced IVB problem, and provide the corresponding error estimates and stability analysis. The delay-dependent dynamical properties on the Nicholson's blowflies equation and the Mackey-Glass equation are numerically investigated. Finally, numerical examples are given to demonstrate the efficiency of our LABCs and theoretical results of the numerical scheme.

Qiumei Huang, Dongfang Li and Jiwei Zhang. (2018). Numerical Investigations of a Class of Biological Models on Unbounded Domain. Numerical Mathematics: Theory, Methods and Applications. 12 (1). 169-186. doi:10.4208/nmtma.OA-2017-0117
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