A method for the numerical solution of singular integral equations with logarithmic singularities

Abstract

A method of numerical solution of singular integral equations of the first kind with logarithmic singularities in their kernels along the integration interval is proposed. This method is based on the reduction of these equations to equivalent singular integral equations with Cauchy-type singularities in their kernels and the application to the latter of the methods of numerical solution, based on the use of an appropriate numerical integration rule for the reduction to a system of linear algebraic equations. The aforementioned method is presented in two forms giving slightly different numerical results. Furthermore, numerical applications of the proposed methods are made. Some further possibilities are finally investigated

Keywords:

• Singular integral equations
• logarithmic singularities
• numerical integration rules
• Chebyshev polynomials
• Cauchy-type singularities
• collocation points
• nodes

C.R. Categories:

• 5.18
• 5.16