Topics in Integral and Integro-Differential Equations: Theory and Applications (Studies in Systems, Decision and Control, 340)

✍ Scribed by Harendra Singh (editor), Hemen Dutta (editor), Marcelo M. Cavalcanti (editor)

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 263
• Category: Library

✦ Synopsis

This book includes different topics associated with integral and integro-differential equations and their relevance and significance in various scientific areas of study and research. Integral and integro-differential equations are capable of modelling many situations from science and engineering. Readers should find several useful and advanced methods for solving various types of integral and integro-differential equations in this book. The book is useful for graduate students, Ph.D. students, researchers and educators interested in mathematical modelling, applied mathematics, applied sciences, engineering, etc.

Key Features

• New and advanced methods for solving integral and integro-differential equations

• Contains comparison of various methods for accuracy

• Demonstrates the applicability of integral and integro-differential equations in other scientific areas

• Examines qualitative as well as quantitative properties of solutions of various types of integral and integro-differential equations

✦ Table of Contents

Preface
Contents
Wavelet-Galerkin Method for Second-Order Integro-differential Equations on Product Domains
1 Introduction
2 Existence and Uniqueness of the Weak Solution
3 Wavelet Bases on Product Domains
3.1 Concept of a Wavelet Basis
3.2 Isotropic Wavelet Bases
3.3 Anisotropic Wavelet Basis
3.4 Construction of Spline Wavelet Bases
4 Wavelet-Galerkin Method
5 Merton Jump-Diffusion Option Pricing Model
6 Numerical Examples
7 Conclusions
References
Analysis and Spectral Element Solution of Nonlinear Integral Equations of Hammerstein Type
1 Introduction
2 Preliminary Assumptions
3 Existence and Uniqueness
4 Spectral Element Approximation
5 Convergence Analysis
5.1 Convergence of the Spectral Element Method
5.2 Convergence of Picard Iteration
5.3 Global Convergence of the Error
6 Numerical Experiments
6.1 Smooth Initial Data
6.2 Smooth Initial Data, Unknown Exact Solution
6.3 Two-Dimensional Hammerstein Equation
6.4 Application to Chemical Reactor Theory
7 Conclusions
References
Approximate Methods for Solving Hypersingular Integral Equations
1 Introduction
2 Continuous Method and Its Convergence Properties
3 Analytical Methods for Solving Hypersingular and Bihypersingular Integral Equations
3.1 Introduction
3.2 Hypersingular Integral Equations
3.3 Bihypersingular Integral Equations
4 Approximate Solution of the First Kind HSIEs
4.1 Introduction
4.2 An Approximate Solution of HSIEs of the First Kind by the Mechanical Quadrature Method
5 An Approximate Solution of Second Kind HSIEs
5.1 An Approximate Solution of Linear HSIEs on Closed Circuits
5.2 An Approximate Solution of Linear HSIEs with Even Order Singularity
6 Summary and Discussion
References
Solutions of Integral Equations by Reproducing Kernel Hilbert Space Method
1 Introduction
2 Preliminaries
3 Reproducing Kernel Hilbert Space Method
4 Solutions of the Problem
5 Applications of the Method
6 Conclusions
References
Restricted Global Convergence Domains for Integral Equations of the Fredholm-Hammerstein Type
1 Introduction
2 Motivation
3 Nemystkii Operator with Bounded Second Derivative
3.1 A First Study of Restricted Global Convergence
3.2 Degree of Logarithmic Convexity Operator
4 Nemystkii Operator with Lipschitz Continuous First Derivative
4.1 Restricted Global Convergence
4.2 Uniqueness of Solution
5 Conclusions
References
Boundary Integral Equation Formulation for Fractional Order Theory of Thermo-Viscoelasticity
1 Introduction
2 The Mathematical Model
3 Formulation in the Laplace Transform Domain
4 Fundamental Solutions in the Laplace Transform Domain
5 Reciprocity Theorem
6 Boundary Integral Equations
7 Example
References
Spectral Methods for Solving Integro-differential Equations and Bibiliometric Analysis
1 Introduction
2 Bibiliometric Analysis
3 Applications
4 Spectral Methods and Integro-differential Equations
4.1 Preliminaries
4.2 Numerical Methods
4.3 Convergence Analysis and Error Estimation
4.4 Numerical Results
5 Conclusion
References
An Efficient Numerical Algorithm to Solve Volterra Integral Equation of Second Kind
1 Introduction
2 Derivation of the Method
2.1 Volterra Runge-Kutta Method (VRK)
2.2 Exponentially-Fitted Volterra-Runge-Kutta (ef-VRK) Method
3 Local Truncation Error
4 Numerical Experiments
5 Conclusion
References
An Integral Equation Method for Wave Scattering by a Pair of Horizontal Porous Plates
1 Introduction
2 Mathematical Formulation
3 Method of Solution
4 Physical Quantities
4.1 Reflection Coefficient and Transmission Coefficient
4.2 Energy Identity
4.3 Hydrodynamic Forces
5 Numerical Results and Discussions
5.1 Results Related to Finite Depth Water
5.2 Results Related to Deep Water
6 Conclusion
References