Comparison of Hybrid Legendre and Hybrid Taylor methods for solving nonlinear Volterre- Fredholm Hammerstein integro- differential Equations

In this paper a numerical method for solving nonlinear Volterra- Fredholm Hammerstein integro-differential equations by two bases Hybrid Legendre and Hybrid Taylor is presented. In this method, we approximate the solution as, where C is unknown coefficients vector and B(x) is known base vector. By using Hybrid functions properties and Gauss-Legendre nodes the coefficients vector C are obtained from a nonlinear equations system. At last, we compare efficiency of two methods through illustrative examples.