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ISBN 10: 1578087104
ISBN 13: 9781578087105
Author: B N Mandal, A Chakrabarti
1. Introduction * Basic Definitions of Integral Equations * Classification of Integral Equations (Volterra, Fredholm, Singular) * Occurrence of Singular Integral Equations in various fields (e.g., Elasticity, Fluid Mechanics, Electromagnetism, Quantum Mechanics) * Weakly Singular Integral Equations (Abel's Problem) * Cauchy Type Singular Integral Equations * Hypersingular Integral Equations
2. Some Elementary Methods of Solution of Singular Integral Equations * Abel Integral Equation and its Generalization * Integral Equations with Logarithmic Type of Singularities * Integral Equations with Cauchy Type Kernels * Applications to Boundary Value Problems in Engineering and Physics
3. Riemann-Hilbert Problems and Their Uses in Singular Integral Equations * Cauchy Principal Value Integrals * Basic Results in Complex Variable Theory (Cauchy's Integral Formula, Liouville's Theorem, etc.) * Solution of Singular Integral Equations involving Closed Contours * General Riemann-Hilbert Problems * Generalized Abel Integral Equations * Singular Integral Equations with Logarithmic Kernels * Singular Integral Equations with Logarithmic Kernels in Disjoint Intervals
4. Special Methods of Solution of Singular Integral Equations * Integral Equations with Logarithmically Singular Kernels * Integral Equations with Cauchy Type Kernels * Use of Poincaré-Bertrand Formula * Solution of Singular Integral Equations involving Two Intervals
5. Hypersingular Integral Equations * Definitions of Hypersingular Integrals * Occurrence of Hypersingular Integral Equations in different contexts * Solution of Simple Hypersingular Integral Equations * Solution of Hypersingular Integral Equations of the Second Kind
6. Singular Integro-Differential Equations * A Class of Singular Integro-Differential Equations * A Special Type of Singular Integro-Differential Equation * Numerical Solutions for Singular Integro-Differential Equations (e.g., polynomial approximation, Bernstein polynomial basis)
7. Galerkin Method and its Application * General Principles of the Galerkin Method * Use of Single-Term Galerkin Approximation * Galerkin Method for Singular Integral Equations
8. Numerical Methods for Singular Integral Equations * General Numerical Procedures for Cauchy Singular Integral Equations * Special Numerical Techniques for First Kind Singular Integral Equations with Cauchy Kernel * Numerical Solution of Hypersingular Integral Equations (e.g., using polynomial expansion, Bernstein polynomials) * Numerical Solution of Logarithmically Singular Integral Equations * Numerical Solution of Systems of Generalized Abel Integral Equations
9. Some Special Types of Coupled Singular Integral Equations (e.g., Carleman Type) and their Solutions
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Tags: B N Mandal, A Chakrabarti, singular, equations
