ABSTRACT
For a given problem, after a mathematical model is developed in the form of a set of governing equations, a solution for the field variables is sought. Analytical solutions for these equations are often not possible to develop for most of the real life practical problems. For these situations, we resort to numerical methods of solution. Among these methods, there is a direct and rather simple one known as the “Finite Difference Method (FDM)”. In this method, the ‘derivatives’ in governing equations are replaced by their approximate “finite difference” relations defined at discrete nodal points of a grid or mesh. Thus, the governing differential equations are transformed (discretized) into a set of algebraic equations, which then are easily solved with the help of computer. Often times FDM is used in conjunction with the Finite Element Method (FEM). For the time-dependent problems, the FDM is used to discretize the temporal derivatives.
In this chapter, the fundamentals of FDM are presented along with applications to few common geotechnical problems such as 1-D consolidation and 2-D steady state seepage.
