Partial differential equations (PDEs) have been developed and used in science and engineering for more than 200 years, yet they remain a very active area of research, because of both their role in mathematics and their application to virtually all areas of science and engineering. This research has been spurred by the relatively recent development of computer solution methods for PDEs. These have extended PDE applications such that we can now quantify broad areas of physical, chemical and biological phenomena.

A large class of models now being actively studied are concerned with traveling waves and are of a type and complexity such that their solutions are usually beyond traditional mathematical analysis. Consequently, numerical methods have to be employed.

This book surveys some of these new developments in analytical and numerical methods and is aimed at senior undergraduates, postgraduates and professionals in the fields of engineering, mathematics and the sciences. It relates these new developments through the exposition of a series of solutions, programmed in Matlab and Maple, to complex PDE problems. The PDEs that have been selected are largely named in the sense that they are generally closely linked to their original contributors. These names usually reflect the fact that the PDEs are widely recognized and are of fundamental importance to the understanding of many application areas.

• Includes line-by-line discussion of the computer code and analysis of the PDE model solutions.