An optimal adaptive time-stepping scheme for solving reaction-diffusion-chemotaxis systems - Chichia Chiu; Jui-Ling Yu (Mathematical Biosciences and Engineering)
Reaction-diffusion-chemotaxis systems have proven to be fairlyaccurate mathematical models for many pattern formation problems in chemistryand biology. These systems are important for computer simulationsof patterns, parameter estimations as well as analysis of the biological systems.To solve reaction-diffusion-chemotaxis systems, efficient and reliablenumerical algorithms are essential for pattern generations. In this paper, ageneral reaction-diffusion-chemotaxis system is considered for specific numericalissues of pattern simulations. We propose a fully explicit discretizationcombined with a variable optimal time step strategy for solving the reactiondiffusion-chemotaxis system. Theorems about stability and convergence of thealgorithm are given to show that the algorithm is highly stable and efficient.Numerical experiment results on a model problem are given for comparisonwith other numerical methods. Simulations on two real biological experimentswill also be shown.