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Methods for Solving Singular Integral Equations of the First Kind
- Some Definitions and Remarks
- Integral Equations of the First Kind with Cauchy Kernel.
- Integral Equations of the First Kind with Hilbert Kernel.
- Cauchy Type Integral
- Definition of the Cauchy Type Integral.
- Hölder Condition.
- Principal Value of a Singular Integral.
- Multivalued Functions.
- Principal Value of a Singular Curvilinear Integral.
- Poincaré-Bertrand Formula.
- Riemann Boundary Value Problem
- Principle of Argument. The Generalized Liouville Theorem.
- Hermite Interpolation Polynomial.
- Notion of the Index.
- Statement of the Riemann Problem.
- Solution of the Homogeneous Problem.
- Solution of the Nonhomogeneous Problem.
- Riemann Problem with Rational Coefficients.
- Riemann Problem for a Half-Plane.
- Exceptional Cases of the Riemann Problem
- Riemann Problem for a Multiply Connected Domain.
- Riemann Problem for Open Curves.
- Riemann Problem with a Discontinuous Coefficient.
- Riemann Problem in the General Case.
- Hilbert Boundary Value Problem.
- Singular Integral Equations of the First Kind
- Simplest Equation with Cauchy Kernel.
- Equation with Cauchy Kernel on the Real Axis.
- Equation of the First Kind on a Finite Interval.
- General Equation of the First Kind with Cauchy Kernel.
- Equations of the First Kind with Hilbert Kernel.
- Multhopp–Kalandiya Method
- Solution That is Unbounded at the Endpoints of the Interval.
- Solution Bounded at One Endpoint of the Interval.
- Solution Bounded at Both Endpoints of the Interval.
- Hypersingular Integral Equations
- Hypersingular Integral Equations with Cauchy- and Hilbert-Type Kernels.
- Definition of Hypersingular Integrals.
- Exact Solution of the Simplest Hypersingular Equation with Cauchy-Type Kernel.
- Exact Solution of the Simplest Hypersingular Equation with Hilbert-Type Kernel.
- Numerical Methods for Hypersingular Equations.
Abstract
A singular integral equation of the first kind with Cauchy kernel has the form
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