ABSTRACT
Partial differential equations (PDEs) play an important role in numerous branches of science and engineering. They describe many types of physical phenomena in science and engineering. PDEs have become a useful tool for describing the nature of science and engineering models. Nowadays, most of the phenomena that arise in mathematical physics and engineering fields can be described by PDEs. Many engineering applications are simulated mathematically as PDEs with initial and boundary conditions. Most physical phenomena in fluid dynamics, quantum mechanics, electricity, and many other fields are described using PDEs. Exact analytical solutions can be obtained in only a few cases, and these analytical methods are rather complicated. However, there are efficient numerical methods to obtain good approximate solutions. Therefore, it becomes increasingly important to be familiar with the numerical methods for solving PDEs and implementing these methods. Among the numerical methods, the finite difference method (FDM) has the attractive feature that it is applicable to linear as well to nonlinear PDEs. In this chapter, we shall discuss FDMs for solving PDEs.
