An algorithm for the solution of a linear system of algebraic equations arising in the mesh method for the Poisson equation

Abstract

From the introduction: We present an algorithm for direct (non-iterative) solution of the system of linear algebraic equations by the finite difference method for the equation Δu(x,y)=f(x,y), (x,y)∈Ω={(x,y):0 0}, u(x,y)=φ(x,y), (x,y)∈∂Ω. O(n2log2n) arithmetical operations are required for arbitrary f,φ, and O(n2) for some special ones, e.g., f≡0, φ arbitrary or φ≡0, f(x,y)≡h(x)g(x), where n is the number of unknowns in the system.''