Universal approaches to approximate biological systems with nonstandard finite difference methods

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• 作者：Daniel T. Wood^a ; ^{dwood@fredhutch.org} ; Hristo V. Kojouharov^b ; ^{hristo@uta.edu} ; Dobromir T. Dimitrov^a ; ^{ddimitro@scharp.org}
• 关键词：Finite difference ; Nonstandard ; Elementary stable ; Positivity ; Dynamically consistent
• 刊名：Mathematics and Computers in Simulation
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：133
• 期：Complete
• 页码：337-350
• 全文大小：1297 K
• 卷排序：133

文摘

Nonstandard finite difference methods have been extensively used to numerically solve various problems in science and engineering. Most of those methods have been specifically designed to handle each problem separately and have been difficult to extend to other problems. In recent years, general nonstandard modeling approaches preserving key characteristics of autonomous dynamical systems have been proposed. In this paper, three of these numerical methods are presented and their performance is evaluated and compared in several different settings.