We develop a computationally less expensive alternative to the direct solution of a large sparse symmetric positive definite system arising from the numerical solution of elliptic partial differential equation models. Our method, substituted factorization , replaces the computationally expensive factorization of certain dense submatrices that arise in the course of direct solution with sparse C...

In this paper, we will discuss the numerical solution of the two dimensional Heat Equation. An approximation to the solution function is calculated at discrete spatial mesh points, proceeding in discrete time steps. The starting values are given by an initial value condition. We will first explain how to transform the differential equation into a finite difference equation, respectively a set o...