Numerical solution of nonlinear Volterra-Fredholm integral equations of the first kind using alternative Legendre polynomials

Alternative Legendre polynomials (ALPs) are used for approximating the solution of nonlinear Volterra-Fredholm integral equations (VFIEs) of the rst kind. The problem is rst transformed into a second kind VFIE and then, using the ALP operational matrices of integration and the product, the solution of the later problem is reduced to the one of solving a system of nonlinear algebraic equations with unknown ALP coecients of the exact solution. An error analysis of the method is given. Results of numerical examples are presented, which illustrate that the proposed method achieve good accuracy even using a small number of ALPs.