A Research on the Numerical Solution of Partial Differential Equations Using Matrix Theory

Exploring the Application of Matrix Theory in Solving Parabolic Partial Differential Equations

Abstract

The study commences with a description and classification of partial differential equations and the related matrix and eigenvalue theory. Almost in all cases the study of parabolic equations leads to initial boundary value problems and it is to this problem that the study is mainly concerned with. This paper will focus on basic (finite difference) methods to solve a (parabolic) partial differential equation. Within the text, it is included various references to distinct detailed reviews that are related to research field in this area.