Paper Title
Numerical Solution of MLPG Method based on Reproducing Kernel Particle Interpolation (RKPI) for Solving Convection-Diffusion equation

The convection-diffusion equation with the non-local boundary conditions arises in many physical phenomena. In this paper, the meshless local Pretrov-Galerkin (MLPG) method based on the reproducing kernel particle interpolation (RKPI) method to solving time-dependent convection-diffusion equation in two-dimensional spaces on a square domain. A technique is proposed to construct shape functions using reproducing kernel function, and the Heaviside step function is used as a test function in each sub-domain to avoid the need for domain integral in local symmetric weak form. The time derivatives are approximated by the Crank-Nicolson method. Numerical experiment is implemented to verify the efficiency, easiness and accuracy of the method. The method can be used to achieve relatively high accuracy, and the essential boundary conditions can be directly enforced. Keywords - MLPG; RKPI, Convection-Diffusion Equation, Crank-Nicolson, Non-Local Boundary Condition.