ABSTRACT
This chapter illustrates with a simple example, the basic steps in the transformation of a problem governed by a differential equation and some specified boundary conditions into a system of algebraic equations. It presents an overview of various methods for solving systems of algebraic equations as well as discusses their advantages and limitations. A large variety of finite difference schemes is available for discretizing the derivatives in differential equations; the choice depends on the nature of the governing differential equation and its boundary conditions. The chapter also illustrates the basic steps in the transformation of a differential equation and its boundary conditions into a set of algebraic equations. It also presents an overview of the direct and iterative methods of solving systems of algebraic equations and discusses the implications of nonlinear systems. The boundary value problems become nonlinear due to the nonlinearity of the governing differential equations or of the boundary conditions or both.
