Half-sweep Modified SOR Approximation of A Two-dimensional Nonlinear Parabolic Partial Differential Equation

Abstract

The sole subject of this numerical analysis was the half-sweep modified successive over-relaxation approach (HSMSOR), which takes the form of an iterative formula. This study computed a class of two-dimensional nonlinear parabolic partial differential equations subject to Dirichlet boundary conditions numerically using the implicit-type finite difference scheme. The computational cost optimization was considered by converting the traditional implicit finite difference approximation into the half-sweep finite difference approximation. The implementation required inner-outer iteration cycles, the second-order Newton method, and a linearization technique. The created HSMSOR is utilized to obtain an approximation of the linearized equations system through the inner iteration cycle. In contrast, the problem's numerical solutions are obtained using the outer iteration cycle. The study examined the local truncation error and the stability, convergence, and method analysis. Results from three initial-boundary value issues showed that the proposed method had competitive computational costs compared to the existing method.