Structure Preserving Numerical Analysis of Reaction-Diffusion Models. (20th March 2022)

• Record Type: Journal Article
• Authors: Ahmed, Nauman; Rehman, Muhammad Aziz-ur; Adel, Waleed; Jarad, Fahd; Ali, Mubasher; Rafiq, Muhammad; Akgül, Ali
• Other Names: Youssri Youssri Hassan Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2022(2022)
• Publication Date: 2022-03-20
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2022/5128343
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : In this paper, we examine two structure preserving numerical finite difference methods for solving the various reaction-diffusion models in one dimension, appearing in chemistry and biology. These are the finite difference methods in splitting environment, namely, operator splitting nonstandard finite difference (OS-NSFD) methods that effectively deal with nonlinearity in the models and computationally efficient. Positivity of both the proposed splitting methods is proved mathematically and verified with the simulations. A comparison is made between proposed OS-NSFD methods and well-known classical operator splitting finite difference (OS-FD) methods, which demonstrates the advantages of proposed methods. Furthermore, we applied proposed NSFD splitting methods on several numerical examples to validate all the attributes of the proposed numerical designs.