Meshless singular boundary method for two-dimensional pseudo-parabolic equation: analysis of stability and convergence

Abstract

In this study, the singular boundary method is applied to solve time-dependent pseudo-parabolic equations in two space dimensions with initial and Dirichlet-type boundary conditions. A splitting procedure is used to split the solution of the inhomogeneous governing equation into a homogeneous solution and a particular solution. This work presents the numerical operation for calculating the particular solution and homogeneous solution. Several numerical examples are provided to show the accuracy and efficiency of the method. Furthermore, the analysis of stability and convergence is presented.