Solution of Linear Equation Systems

Abstract

In the previous two chapters we showed how the convection-diffusion equation may be discretized using FD and FV methods. In either case, the result of the discretization process is a system of algebraic equations, which are linear or non-linear according to the nature of the partial differential equation(s) from which they are derived. In the non-linear case, the discretized equations must be solved by an iterative technique that involves guessing a solution, linearizing the equations about that solution, and improving the solution; the process is repeated until a converged result is obtained. So, whether the equations are linear or not, efficient methods for solving linear systems of algebraic equations are needed.