## Abstract

In Chapter 1, it was indicated that many phenomena of physics and engineering are expressed by partial differential equations PDEs. The PDE is termed a *Boundary Value Problem* (BVP) if the boundary conditions of the dependent variable *u* and some of its partial derivatives are often prescribed. However, the PDE is called an *Initial Value Problem* (IVP) if the initial conditions of the dependent variable *u* are prescribed at the starting time *t*=0. Moreover, the PDE is termed *Initial-Boundary Value Problem* (IBVP) if both initial conditions and boundary conditions are prescribed.

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