RBFs meshless method of lines for time dependent PDEs with decomposition of interior and boundary data centers

Abstract

The meshless method of lines (MOL) is proposed for the numerical solution of time dependent partial differential equations (PDEs). After approximating spatial derivatives of equation and boundary condition by radial basis functions the resulting system will be a system of differential-algebraic equations. The differential-algebraic equation is converted to a system of ordinary differential equations (ODEs) by decomposing of interior and boundary centers and replacing expansion coeffcients of boundary centers as a function of interior ones. Computational experiments are performed for two-dimensional Burgers' equations and Brusselator reaction-diffusion system. The numerical results compete very well with the analytical solutions.