%0 Journal Article %A Jyh-Yang Wu and Sheng-Gwo Chen %D 2016 %J International Journal of Mathematical and Computational Sciences %B World Academy of Science, Engineering and Technology %I Open Science Index 119, 2016 %T A Numerical Method for Diffusion and Cahn-Hilliard Equations on Evolving Spherical Surfaces %U https://publications.waset.org/pdf/10005661 %V 119 %X In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations. %P 551 - 559