Page 19 - Handbook Of Integral Equations

11.8. Methods of Integral Transforms and Model Solutions
11.8-1. Equation With Difference Kernel on the Entire Axis
–1
11.8-2. An Equation With the Kernel K(x, t)= t Q(x/t) on the Semiaxis
β
11.8-3. Equation With the Kernel K(x, t)= t Q(xt) on the Semiaxis
11.8-4. The Method of Model Solutions for Equations on the Entire Axis
11.9. The Carleman Method for Integral Equations of Convolution Type of the Second Kind
11.9-1. The Wiener–Hopf Equation of the Second Kind
11.9-2. An Integral Equation of the Second Kind With Two Kernels
11.9-3. Equations of Convolution Type With Variable Integration Limit
11.9-4. Dual Equation of Convolution Type of the Second Kind
11.10. The Wiener–Hopf Method
11.10-1. Some Remarks
11.10-2. The Homogeneous Wiener–Hopf Equation of the Second Kind
11.10-3. The General Scheme of the Method. The Factorization Problem
11.10-4. The Nonhomogeneous Wiener–Hopf Equation of the Second Kind
11.10-5. The Exceptional Case of a Wiener–Hopf Equation of the Second Kind
11.11. Krein’s Method for Wiener–Hopf Equations
11.11-1. Some Remarks. The Factorization Problem
11.11-2. The Solution of the Wiener–Hopf Equations of the Second Kind
11.11-3. The Hopf–Fock Formula
11.12. Methods for Solving Equations With Difference Kernels on a Finite Interval
11.12-1. Krein’s Method
11.12-2. Kernels With Rational Fourier Transforms
11.12-3. Reduction to Ordinary Differential Equations
11.13. The Method of Approximating a Kernel by a Degenerate One
11.13-1. Approximation of the Kernel
11.13-2. The Approximate Solution
11.14. The Bateman Method
11.14-1. The General Scheme of the Method
11.14-2. Some Special Cases
11.15. The Collocation Method
11.15-1. General Remarks
11.15-2. The Approximate Solution
11.15-3. The Eigenfunctions of the Equation
11.16. The Method of Least Squares
11.16-1. Description of the Method
11.16-2. The Construction of Eigenfunctions
11.17. The Bubnov–Galerkin Method
11.17-1. Description of the Method
11.17-2. Characteristic Values
11.18. The Quadrature Method
11.18-1. The General Scheme for Fredholm Equations of the Second Kind
11.18-2. Construction of the Eigenfunctions
11.18-3. Specific Features of the Application of Quadrature Formulas
11.19. Systems of Fredholm Integral Equations of the Second Kind
11.19-1. Some Remarks
11.19-2. The Method of Reducing a System of Equations to a Single Equation

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
Page xix