The research project is concerned with the numerical solution of several classes of linear and nonlinear integral equations. Specific types of integral equations slated for study include linear and nonlinear boundary integral equations, nonlinear Urysohn equations and nonlinear Fredholm equations. Such equations arise in a host of pure and applied areas, and one of the goals of the research is the development of multi-purpose codes that can be fitted into software routines to enable researchers from many different disciplines to solve these integral equations efficiently and accurately. Very often the solution of a problem in mathematical physics or mathematical biology can be expressed in the form of an integral equation. However this does not mean that the problem is solved; rather, the resulting integral equation must be solved either analytically or numerically. In this proposal the researchers will improve existing numerical schemes and develop new ones in order to produce multi-purpose software for the approximate solution of several types of integral equations in several space dimensions.
