A Novel Spatio-Temporal Fully Meshless Method for Parabolic PDEs

Abstract

We introduce a meshless method derived by considering the time variable as a spatial variable without the need to extend further conditions to the solution of linear and non-linear parabolic PDEs. The method is based on a moving least squares method, more precisely, the generalized finite difference method (GFDM), which allows us to select well-conditioned stars. Several 2D and 3D examples, including the time variable, are shown for both regular and irregular node distributions. The results are compared with explicit GFDM both in terms of errors and execution time.