Structure Preserving Numerical Analysis of Reaction-Diffusion Models. (20th March 2022) - Ahmed, Nauman; Rehman, Muhammad Aziz-ur; Adel, Waleed; Jarad, Fahd; Ali, Mubasher; Rafiq, Muhammad; Akgül, Ali
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.