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Linear and Nonlinear Integral Equations : Methods and Applications / by Abdul-Majid Wazwaz
Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: SpringerLink BücherPublisher: Berlin, Heidelberg : Higher Education Press, Beijing and Springer-Verlag GmbH Berlin Heidelberg, 2011Description: Online-Ressource (XVIII, 639p. 4 illus, digital)ISBN:- 9783642214493
- 1283476231
- 9781283476232
- 515.45 515/.45
- 515.45
- QA431
- QA431 .W39 2011
Contents:
Summary: PART I: Linear Integral Equations. Preliminaries -- Introductory Concepts of Integral Equations -- Volterra Integral Equations -- Fredholm Integral Equations -- Volterra Integro-Differential Equations -- Fredholm Integro-Differential Equations -- Abel’s Integral Equation and Singular Integral Equations -- Volterra-Fredholm Integral Equations -- Volterra-Fredholm Integro-Differential Equations -- Systems of Volterra Integral Equations -- Systems of Fredholm Integral Equations.-Systems of Singular Integral Equations. PART II: Nonlinear Integral Equations. Nonlinear Volterra Integral Equations -- Nonlinear Volterra Integro-Differential Equations -- Nonlinear Fredholm Integral Equations -- Nonlinear Fredholm Integro-Differential Equations -- Nonlinear Singular Integral Equations -- Applications of Integral Equations.Summary: 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. .PPN: PPN: 1651069107Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
Title Page; Copyright Page; Preface; Table of Contents; Part I Linear Integral Equations; Chapter 1 Preliminaries; 1.1 Taylor Series; 1.2 Ordinary Differential Equations; 1.2.1 First Order Linear Differential Equations; 1.2.2 Second Order Linear Differential Equations; 1.2.3 The Series Solution Method; 1.3 Leibnitz Rule for Differentiation of Integrals; 1.4 Reducing Multiple Integrals to Single Integrals; 1.5 Laplace Transform; 1.5.1 Properties of Laplace Transforms; 1.6 Infinite Geometric Series; References; Chapter 2 Introductory Concepts of Integral Equations
2.1 Classification of Integral Equations2.1.1 Fredholm Integral Equations; 2.1.2 Volterra Integral Equations; 2.1.3 Volterra-Fredholm Integral Equations; 2.1.4 Singular Integral Equations; 2.2 Classification of Integro-Differential Equations; 2.2.1 Fredholm Integro-Differential Equations; 2.2.2 Volterra Integro-Differential Equations; 2.2.3 Volterra-Fredholm Integro-Differential Equations; 2.3 Linearity and Homogeneity; 2.3.1 Linearity Concept; 2.3.2 Homogeneity Concept; 2.4 Origins of Integral Equations; 2.5 Converting IVP to Volterra Integral Equation
2.5.1 Converting Volterra Integral Equation to IVP2.6 Converting BVP to Fredholm Integral Equation; 2.6.1 Converting Fredholm Integral Equation to BVP; 2.7 Solution of an Integral Equation; References; Chapter 3 Volterra Integral Equations; 3.1 Introduction; 3.2 Volterra Integral Equations of the Second Kind; 3.2.1 The Adomian Decomposition Method; 3.2.2 The Modified Decomposition Method; 3.2.3 The Noise Terms Phenomenon; 3.2.4 The Variational Iteration Method; 3.2.5 The Successive Approximations Method; 3.2.6 The Laplace Transform Method; 3.2.7 The Series Solution Method
3.3 Volterra Integral Equations of the First Kind3.3.1 The Series Solution Method; 3.3.2 The Laplace Transform Method; 3.3.3 Conversion to a Volterra Equation of the Second Kind; References; Chapter 4 Fredholm Integral Equations; 4.1 Introduction; 4.2 Fredholm Integral Equations of the Second Kind; 4.2.1 The Adomian Decomposition Method; 4.2.2 The Modified Decomposition Method; 4.2.3 The Noise Terms Phenomenon; 4.2.4 The Variational Iteration Method; 4.2.5 The Direct Computation Method; 4.2.6 The Successive Approximations Method; 4.3 Homogeneous Fredholm Integral Equation
4.3.1 The Direct Computation Method4.4 Fredholm Integral Equations of the First Kind; 4.4.1 The Method of Regularization; 4.4.2 The Homotopy Perturbation Method; References; Chapter 5 Volterra Integro-Differential Equations; 5.1 Introduction; 5.2 Volterra Integro-Differential Equations of the Second Kind; 5.2.1 The Adomian Decomposition Method; 5.2.2 The Variational Iteration Method; 5.2.3 The Laplace Transform Method; 5.2.4 The Series Solution Method; 5.2.5 Converting Volterra Integro-Differential Equations to Initial Value Problems
5.2.6 ConvertingVolterra Integro-Differential Equation to Volterra Integral Equation
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