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

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

1st Edition - November 4, 2015

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  • Authors: T Jangveladze, Z Kiguradze, Beny Neta
  • Hardcover ISBN: 9780128046289
  • eBook ISBN: 9780128046692

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Description

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.

Key Features

  • 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

Readership

Scientists working in the field of nonlinear integro-differential models, mathematical physicists, and applied and numerical mathematicians, and also MS and PhD students of the appropriate specializations

Table of Contents

  • Preface

    Acknowledgments

    Abstract

    Chapter 1: Introduction

    • Abstract
    • 1.1 Comments and bibliographical notes

    Chapter 2: Mathematical Modeling

    • Abstract
    • 2.1 Electromagnetic diffusion process
    • 2.2 On the averaged Model II
    • 2.3 Mathematical Model III
    • 2.4 Some features of Models I and II
    • 2.5 Some features of Model III
    • 2.6 Comments and bibliographical notes
    • 2.2 On the averaged Model II
    • 2.3 Mathematical Model III
    • 2.5 Some features of Model III

    Chapter 3: Approximate Solutions of the Integro-Differential Models

    • Abstract
    • 3.1 Semi-discrete scheme for Model I
    • 3.2 Finite difference scheme for Model I
    • 3.3 Semi-discrete scheme for Model II
    • 3.4 Finite difference scheme for Model II
    • 3.5 Discrete analogues of Model III
    • 3.6 Galerkin’s method for Model I
    • 3.7 Galerkin’s method for Model II
    • 3.8 Galerkin’s method for Model III
    • 3.9 Comments and bibliographical notes
    • 3.1 Semi-discrete scheme for Model I
    • 3.2 Finite difference scheme for Model I
    • 3.3 Semi-discrete scheme for Model II
    • 3.4 Finite difference scheme for Model II
    • 3.5 Deserete analogues of Model III
    • 3.6 Galerkin’s method for Model I
    • 3.7 Galerkin’s method for Model II
    • 3.8 Galerkin’s method for Model III

    Chapter 4: Numerical Realization of the Discrete Analogous for Models I-III

    • Abstract
    • 4.1 Finite difference solution of Model I
    • 4.2 Finite difference solution of Model II
    • 4.3 Galerkin’s solution of Model II
    • 4.4 Finite difference solution of Model III
    • 4.5 Comments and bibliographical notes
    • 4.1 Numerical solution of Model I
    • 4.2 Numerical solution of Model II
    • 4.3 Numerical solution of Model III

    Bibliography

    Index

Product details

  • No. of pages: 254
  • Language: English
  • Copyright: © Academic Press 2015
  • Published: November 4, 2015
  • Imprint: Academic Press
  • Hardcover ISBN: 9780128046289
  • eBook ISBN: 9780128046692

About the Authors

T Jangveladze

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

Affiliations and Expertise

Georgia Technical University, Tbilisi, Georgia

Z Kiguradze

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.

Affiliations and Expertise

Tbilisi State University, Tbilisi, Georgia

Beny Neta

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.

Affiliations and Expertise

Naval Postgraduate School, Monterey, CA, USA

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