Open AccessAn optimal adaptive time-stepping scheme for solving reaction-diffusion-chemotaxis systems
Author(s) -
Chichia Chiu,
Jui Ling Yu
Publication year - 2007
Publication title -
mathematical biosciences and engineering
Language(s) - Uncategorized
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2007.4.187
Subject(s) - reaction–diffusion system , discretization , chemotaxis , convergence (economics) , stability (learning theory) , diffusion , computer science , mathematical optimization , numerical analysis , mathematics , mathematical analysis , physics , chemistry , biochemistry , receptor , machine learning , economics , thermodynamics , economic growth
Reaction-diffusion-chemotaxis systems have proven to be fairly accurate mathematical models for many pattern formation problems in chemistry and biology. These systems are important for computer simulations of patterns, parameter estimations as well as analysis of the biological systems. To solve reaction-diffusion-chemotaxis systems, efficient and reliable numerical algorithms are essential for pattern generations. In this paper, a general reaction-diffusion-chemotaxis system is considered for specific numerical issues of pattern simulations. We propose a fully explicit discretization combined with a variable optimal time step strategy for solving the reaction-diffusion-chemotaxis system. Theorems about stability and convergence of the algorithm are given to show that the algorithm is highly stable and efficient. Numerical experiment results on a model problem are given for comparison with other numerical methods. Simulations on two real biological experiments will also be shown.