Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular Kernels

We develop a generalized jacobi-galerkin method for second kind volterra integral equations with weakly singular kernels. in this method,we first introduce some known singular nonpolynomial functions in the approximation space of the conventional jacobi-galerkin method. secondly,we use the gauss-jacobi quadrature rules to approximate the integral term in the resulting equation so as to obtain high-order accuracy for the approximation. then,we establish that the approximate equation has a unique solution and the approximate solution arrives at an optimal convergence order. one numerical example is presented to demonstrate the effectiveness of the proposed method. copyright © 2017 haotao cai.