Introduction

In many mathematical modeling formulations, partial derivatives are required to represent physical quantities. These derivatives always involve more than one independent variable, generally the space variables x, y, . . . and the time variable t. Such formulations have one or more dependent variables, which are the unknown functions of the independent variables. The resulting equations are called partial differential equations , which, together with the initial and/or boundary conditions, represent physical phenomena and are known as the initial or boundary value problems.