COMPARATIVE ANALYSIS OF METHODS FOR SOLVING SINGULAR INTEGRAL EQUATION OF THE SECOND KIND

Abstract

Solving singular integral equations (SIEs-2) of the second kind poses a distinct mathematical computation challenge because the unknown function appears both inside and outside the integral. Several numerical methods can be employed to solve this problem but it mostly involves rigorous numerical computations. Methods like the Chebyshev, Bernstain and Legendre polynomial method can be used to solve SIEs-2 but questions like; which method is best suitable, which method is cheaper and more accurate, are left unanswered. This study compares and analyses these three methods, namely: Legendre polynomials, Chebyshev polynomials and Bernstein polynomials. Using the developed methods, three (3) relevant examples were solved and the results were compared for error and accuracy. The analysis highlights the effectiveness of orthogonal polynomial method and the results show that the Chebyshev method gives a better approximation than the Bernstain and Legendre method in terms of convergence and accuracy.