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

ISBN-13: 9780128046289 / Angielski / Twarda / 2015 / 254 str.

Jangveladze, T Kiguradze, Z Neta, Beny

Opis

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.

• Investigations of the described equations include theoretical as well as approximation properties
• Detailed references enable further independent study
• Easily understandable proofs describe real-world processes with mathematical rigor

Recenzje

"...useful to scientists working in the eld of nonlinear integro-di erential models, in mathematical physics and numerical mathematics." --Zentralblatt MATH

Spis treści

1. Introduction2. Mathematical Modeling3. Approximate Solutions of the Integro-Differential Models4. Numerical Realization of the Discrete Analogue for Models I - III

O autorze

Temur Jangveladze (Georgia Technical University, Tbilisi, Georgia), is interested in differential and integro-differential equations and systems; nonlinear equations and systems of mathematical physics; mathematical modeling; numerical analysis; nonlocal boundary value problems; nonlocal initial value problems Zurab Kiguradze (Tbilisi State University, Tbilisi, Georgia) is interested in numerical analysis; nonlinear equations and systems of mathematical physics; differential and integro-differential equations and systems; numerical solutions of differential and integro-differential equations and systems; programming. Beny Neta (Naval Postgraduate School, Monterey, CA) is interested in finite elements, orbit prediction, partial differential equations, numerical solutions of ODE, shallow water equations and parallel computing.