Save up to 30% on Elsevier print and eBooks with free shipping. No promo code needed.
Save up to 30% on print and eBooks.
Numerical Solutions of Three Classes of Nonlinear Parabolic Integro-Differential Equations
1st Edition - November 4, 2015
Authors: T Jangveladze, Z Kiguradze, Beny Neta
Language: English
Hardback ISBN:9780128046289
9 7 8 - 0 - 1 2 - 8 0 4 6 2 8 - 9
eBook ISBN:9780128046692
9 7 8 - 0 - 1 2 - 8 0 4 6 6 9 - 2
This book describes three classes of nonlinear partial integro-differential equations. These models arise in electromagnetic diffusion processes and heat flow in materials with me…Read more
Purchase options
LIMITED OFFER
Save 50% on book bundles
Immediately download your ebook while waiting for your print delivery. No promo code is needed.
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
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
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
No. of pages: 254
Language: English
Edition: 1
Published: November 4, 2015
Imprint: Academic Press
Hardback ISBN: 9780128046289
eBook ISBN: 9780128046692
TJ
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
ZK
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
BN
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
Read Numerical Solutions of Three Classes of Nonlinear Parabolic Integro-Differential Equations on ScienceDirect