Solutions of convolution integral and integral equations via double general orthogonal polynomials

Abstract

Double general orthogonal polynomials are developed in this work to approximate the solutions of convolution integrals, Volterra integral equations, and Fredholm integral equations. The proposed method reduces the computations of integral equations to the successive solution of a set of linear algebraic equations in matrix form; thus, the computational complexity is considerably simplified. Furthermore, the solutions obtained by the general orthogonal polynomials include as special cases solutions by Chebyshev polynomials, Legendre polynomials, Laguerre polynomials, or Jacobi polynomials. A comparison of the results obtained via several different classical orthogonal polynomial approximations is also presented.