Page 17 - Handbook Of Integral Equations

9.6-4. The Model Solution in the Case of a Power-Law Right-Hand Side
9.6-5. The Model Solution in the Case of a Sine-Shaped Right-Hand Side
9.6-6. The Model Solution in the Case of a Cosine-Shaped Right-Hand Side
9.6-7. Some Generalizations
9.7. Method of Differentiation for Integral Equations
9.7-1. Equations With Kernel Containing a Sum of Exponential Functions
9.7-2. Equations With Kernel Containing a Sum of Hyperbolic Functions
9.7-3. Equations With Kernel Containing a Sum of Trigonometric Functions
9.7-4. Equations Whose Kernels Contain Combinations of Various Functions
9.8. Reduction of Volterra Equations of the 2nd Kind to Volterra Equations of the 1st Kind
9.8-1. The First Method
9.8-2. The Second Method
9.9. The Successive Approximation Method
9.9-1. The General Scheme
9.9-2. A Formula for the Resolvent
9.10. Method of Quadratures
9.10-1. The General Scheme of the Method
9.10-2. Application of the Trapezoidal Rule
9.10-3. The Case of a Degenerate Kernel
9.11. Equations With Infinite Integration Limit
9.11-1. An Equation of the Second Kind With Variable Lower Integration Limit
9.11-2. Reduction to a Wiener–Hopf Equation of the Second Kind
b

10. Methods for Solving Linear Equations of the Form K(x, t)y(t) dt = f(x)
a
10.1. Some Definition and Remarks
10.1-1. Fredholm Integral Equations of the First Kind
10.1-2. Integral Equations of the First Kind With Weak Singularity
10.1-3. Integral Equations of Convolution Type
10.1-4. Dual Integral Equations of the First Kind
10.2. Krein’s Method
10.2-1. The Main Equation and the Auxiliary Equation
10.2-2. Solution of the Main Equation
10.3. The Method of Integral Transforms
10.3-1. Equation With Difference Kernel on the Entire Axis
10.3-2. Equations With Kernel K(x, t)= K(x/t) on the Semiaxis
10.3-3. Equation With Kernel K(x, t)= K(xt) and Some Generalizations
10.4. The Riemann Problem for the Real Axis
10.4-1. Relationships Between the Fourier Integral and the Cauchy Type Integral
10.4-2. One-Sided Fourier Integrals
10.4-3. The Analytic Continuation Theorem and the Generalized Liouville Theorem
10.4-4. The Riemann Boundary Value Problem
10.4-5. Problems With Rational Coefficients
10.4-6. Exceptional Cases. The Homogeneous Problem
10.4-7. Exceptional Cases. The Nonhomogeneous Problem
10.5. The Carleman Method for Equations of the Convolution Type of the First Kind
10.5-1. The Wiener–Hopf Equation of the First Kind
10.5-2. Integral Equations of the First Kind With Two Kernels

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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