A novel space–time meshless method for nonhomogeneous convection–diffusion equations with variable coefficients. (June 2019) - Yue, Xingxing; Wang, Fajie; Hua, Qingsong; Qiu, Xiang-Yun
Abstract: A new space–time meshless method is proposed for solving the nonhomogeneous convection–diffusion equations with variable coefficients. From the perspective of the space–time distance, the space–time radial basis function in a space and time scale framework is presented and then is employed to discretize the time-dependent parabolic partial differential equations. The present meshless scheme is a truly meshless method which requires neither domain or boundary discretization, and can be easily used for 1D, 2D, and 3D problems. Furthermore, the proposed new methodology does not require the discretization of the temporal derivatives, and therefore is very simple mathematically, relatively fast computationally, and easy to program. Numerical examples conform the effectiveness and accuracy of the proposed method.