Numerical solution of Volterra-Fredholm integral equations using the collocation method based on a special form of the Müntz-Legendre polynomials

This paper presents a computational technique based on a special family of the Müntz-Legendre polynomials to solve a class of Volterra-Fredholm integral equations. The relationship between the Jacobi polynomials and Müntz-Legendre polynomials, in a particular state, are expressed. The proposed method reduces the integral equation into algebraic equations via the Chebyshev-Gauss-Lobatto points, so that the system matrix coefficients are obtained by the least squares approximation method. The useful properties of the Jacobi polynomials are exploited to analyze the approximation error. The performance and accuracy of our method are examined with some illustrative examples.