International Journal of Engineering and Technology

A new polynomial method to solve Volterra–Fredholm Integral equations is presented in this work. The method is based upon Shifted Legendre Polynomials. The properties of Shifted Legendre Polynomials and together with Gaussian integration formula are presented and are utilized to reduce the computation of Volterra–Fredholm Integral equations to a system of algebraic equations. Some numerical examples are selected to illustrate the proposed method also the theoretical analysis of shifted Legendre polynomial method such as convergence and error analysis has been discussed. The results demonstrate reliability and efficiency of the proposed method.