Numerical and Approximation Methods

Abstract

The preceding chapters have been devoted to the analytical treatment of linear and nonlinear partial differential equations. Several analytical methods to find the exact analytical solution of these equations within simple domains have been discussed. The boundary and initial conditions in these problems were also relatively simple, and were expressible in simple mathematical form. In dealing with many equations arising from the modelling of physical problems, the determination of such exact solutions in a simple domain is a formidable task even when the boundary and/or initial data are simple. It is then necessary to resort to numerical or approximation methods in order to deal with the problems that cannot be solved analytically. In view of the widespread accessibility of today’s high speed electronic computers, numerical and approximation methods are becoming increasingly important and useful in applications.