Approximate Solution Technique for Singular Fredholm Integral Equations of the First Kind with Oscillatory Kernels
Vivian Ndfutu Nfor *
Department of Fundamental Science, Higher Technical Teacher Training College Bambili, The University of Bamenda, North West Region, Cameroon.
George Emese Okecka
Department of Mathematics, University of Calabar, P.M.B. 115 Calabar, Cross River State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
An efficient quadrature formula was developed for evaluating numerically certain singular Fredholm integral equations of the first kind with oscillatory trigonometric kernels. The method is based on the Lagrange interpolation formula and the orthogonal polynomial considered are the Legendre polynomials whose zeros served as interpolation nodes. A test example was provided for the verification and validation of the rule developed. The results showed the convergence of the solution and can be improved by increasing n.
Keywords: Singular kernel, oscillatory kernel, lagrange interpolation, orthogonal polynomial, legendre polynomial.