Excellence in Research and Innovation for Humanity
%0 Journal Article
%A Mei-Hsiu Chi and  Jyh-Yang Wu and  Sheng-Gwo Chen
%D 2016 
%J  International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering
%B World Academy of Science, Engineering and Technology
%I International Science Index 119, 2016
%T A Study of Numerical Reaction-Diffusion Systems on Closed Surfaces
%U http://waset.org/publications/10005660
%V 119
%X The diffusion-reaction equations are important Partial Differential Equations in mathematical biology, material science, physics, and so on. However, finding efficient numerical methods for diffusion-reaction systems on curved surfaces is still an important and difficult problem. The purpose of this paper is to present a convergent geometric method for solving the reaction-diffusion equations on closed surfaces by an O(r)-LTL configuration method. The O(r)-LTL configuration method combining the local tangential lifting technique and configuration equations is an effective method to estimate differential quantities on curved surfaces. Since estimating the Laplace-Beltrami operator is an important task for solving the reaction-diffusion equations on surfaces, we use the local tangential lifting method and a generalized finite difference method to approximate the Laplace-Beltrami operators and we solve this reaction-diffusion system on closed surfaces. Our method is not only conceptually simple, but also easy to implement.
%P 543 - 550