On kalandiya’ method for the numerical solution of singular integral equations

Abstract

For the numerical solution of one-dimensional singular integral equations with Cauchy type kernels, one can use an appropriate quadrature rule and an appropriate set of collocation points for the reduction of this equation to a system of linear equations. In this short paper, we use as collocation points the nodes of the quadrature rule and we rederive, in a more direct manner, Kalandiya’ method for the numerical solution of the aforementioned class of equations, which was originally based on a trigonometric interpolation formula. Furthermore, we test this method in numerical applications. Finally, a discussion on the accuracy of the same method is made.

Keywords:

• Cauchy type singular integral equations
• Kalandiya’ method
• principal value integrals
• quadrature rules
• Chebyshev polynomials
• Gauss-Chebyshev quadrature rule
• Lagrangian and trigonometric interpolation formulae

C.R. Categories::

• Primary, 5.18
• secondary, 5.16