Exact Inversion of Pentadiagonal Matrix for Semi-Analytic Solution of 2D Poisson Equation

Abstract

This work essentially consists in inverting in an exact, explicit, and original way the pentadiagonal Toeplitz matrix or tridiagonal block matrix resulting from the discretization of the two-dimensional Laplace operator. This method is an algorithm facilitating the resolution of a large number of problems governed by PDEs involving the Laplacian in two dimensions. It guarantees high precision and high efficiency in solving various differential equations.