ABSTRACT
This chapter presents the two most common of the modern modeling techniques are the finite-difference technique. It deals with some simple examples and develops some simple finite-difference approximations to the derivatives that appear in differential equation descriptions of physical processes. In the finite-difference approach to computational mechanics, it is assumed that the governing equations, in the form of differential equations, are known. The role of numerical computation is to obtain accurate values for the dependent variables of these equations for the region of interest. Careful numerical modeling is required when the boundary of the region is complex and when the material properties of the solid or the fluid are nonhomogeneous or nonisotropic. The chapter discusses a technique that allows it to calculate finite-difference approximations for any order derivative to any desired accuracy. With these approximations, any differential equation can be approximated to the desired order of accuracy.
