TITLE:
Exact Inversion of Pentadiagonal Matrix for Semi-Analytic Solution of 2D Poisson Equation
AUTHORS:
Serigne Bira Gueye
KEYWORDS:
Block Matrix, Pentadiagonal Matrix, 2D Laplacian, Toeplitz Matrix, Inversion
JOURNAL NAME:
Journal of Modern Physics,
Vol.13 No.12,
December
27,
2022
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.