Convergence of Numerical Method For the Solution of Nonlinear Delay Volterra Integral Equations

In this paper, Solvability nonlinear Volterra integral equations with general vanishing delays is stated. So far sinc methods for approximating the solutions of Volterra integral equations have received considerable attention mainly due to their high accuracy. These approximations converge rapidly to the exact solutions as number sinc points increases. Here the numerical solution of nonlinear delay Volterra integral equations is considered by two methods. The methods are developed by means of the sinc approximation with the single exponential (SE) and double exponential (DE) transformations. These numerical methods combine a sinc collocation method with the Newton iterative process that involves solving a nonlinear system of equations. The existence and uniqueness of numerical solutions for these equations are provided. Also an error analysis for the methods is given. So far approximate solutions with polynomial convergence have been reported for this equation. These methods improve conventional results and achieve exponential convergence. Numerical results are included to confirm the efficiency and accuracy of the methods.