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 equations and boundary conditions 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 interior and boundary centers and replacing expansion coefficients 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.
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