Efficient BTCS + CTCS Finite Difference Scheme for General Linear Second Order PDE

Abstract

This work deals with a second order linear general equation with partial derivatives for a two-variable function. It covers a wide range of applications. This equation is solved with a finite difference hybrid method: BTCS + CTCS. This scheme is simple, precise, and economical in terms of time and space occupancy in memory.

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

“…Concerning the matrix D, its inverse is obtained with its cofactors. The inversion of a tridiagonal Toeplitz matrix has been covered in detail in [2] [3] [4] [5].…”

“…Apart from these values i d , the matrix D is regular and its inverse B is symmetric, persymmetric, and is given by the following formula [2] [3] [4] [5]:…”