Numerical Solutions Of Three Classes Of Nonlinear Parabolic Integro Differential Equations
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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. - 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
Linear and Nonlinear Integral Equations
Author: Abdul-Majid Wazwaz
language: en
Publisher: Springer Science & Business Media
Release Date: 2011-11-24
Linear and Nonlinear Integral Equations: Methods and Applications is a self-contained book divided into two parts. Part I offers a comprehensive and systematic treatment of linear integral equations of the first and second kinds. The text brings together newly developed methods to reinforce and complement the existing procedures for solving linear integral equations. The Volterra integral and integro-differential equations, the Fredholm integral and integro-differential equations, the Volterra-Fredholm integral equations, singular and weakly singular integral equations, and systems of these equations, are handled in this part by using many different computational schemes. Selected worked-through examples and exercises will guide readers through the text. Part II provides an extensive exposition on the nonlinear integral equations and their varied applications, presenting in an accessible manner a systematic treatment of ill-posed Fredholm problems, bifurcation points, and singular points. Selected applications are also investigated by using the powerful Padé approximants. This book is intended for scholars and researchers in the fields of physics, applied mathematics and engineering. It can also be used as a text for advanced undergraduate and graduate students in applied mathematics, science and engineering, and related fields. Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University in Chicago, Illinois, USA.
Mathematics, Informatics, and Their Applications in Natural Sciences and Engineering
This book presents eleven peer-reviewed papers from the 3rd International Conference on Applications of Mathematics and Informatics in Natural Sciences and Engineering (AMINSE2017) held in Tbilisi, Georgia in December 2017. Written by researchers from the region (Georgia, Russia, Turkey) and from Western countries (France, Germany, Italy, Luxemburg, Spain, USA), it discusses key aspects of mathematics and informatics, and their applications in natural sciences and engineering. Featuring theoretical, practical and numerical contributions, the book appeals to scientists from various disciplines interested in applications of mathematics and informatics in natural sciences and engineering.