COLLOCATION TECHNIQUE FOR THE NUMERICAL SOLUTION OF THREE DIMENSIONAL VOLTERRA AND FREDHOLM INTEGRAL EQUATIONS BY ORTHOGONAL BASIS FUNCTION

In this paper, standard collocation approximation method is proposed for solving three-dimensional integral equations. New orthogonal polynomials were constructed and used as basis function that gives less rigorous works in terms of computational efforts and enhanced accuracy, Power series and Legendre Polynomials were used as alternative basis functions to checkmate the results of the new Orthogonal Polynomials constructed and used; therefore, three variants of basis functions were used in this work. The proposed methods changed the three-dimensional Volterra and Fredholm integral equations into algebraic system of equations with some unknown constants that were obtained by using MAPLE 18 software. Some numerical examples were solved and less computational works were achieved and the results obtained were in good agreements using three variants with the results available in the literature using different approaches.