Numerical Solutions of Three Classes of Nonlinear Parabolic Integro-Differential Equations

This book describes three classes of nonlinear partial integro-differential equations. These models arise in electromagnetic diffusion processes and heat flow in materials with memory. Mathematical modeling of these processes is briefly described in the first chapter of the book. Investigations of the described equations include theoretical as well as approximation properties. Qualitative and quantitative properties of solutions of initial-boundary value problems are performed therafter. All statements are given with easy understandable proofs. For approximate solution of problems different varieties of numerical methods are investigated. Comparison analyses of those methods are carried out. For theoretical results the corresponding graphical illustrations are included in the book. At the end of each chapter topical bibliographies are provided.

1. Introduction 2. Mathematical Modeling 3. Approximate Solutions of the Integro-Differential Models 4. Numerical Realization of the Discrete Analogue for Models I - III