A collocation procedure is developed for the linear and nonlinear Volterra integral equations, using the globally defined Sinc and auxiliary basis functions. We analytically show the exponential convergence of the Sinc collocation method for approximate solution of Volterra integral equations. Numerical examples are included to confirm applicability and justify rapid convergence of our method.

this paper describes an approximating solution, based on lagrange interpolation and spline functions, to treat functional integral equations of fredholm type and volterra type. this method can be extended to functional dierential and integro-dierential equations. for showing eciency of the method we give some numerical examples.

This article aims at preferring a new and viable algorithm, specifically a two-step homotopy perturbation transform algorithm (TSHPTA). This novel technique is a feasible way in finding exact solutions with a small amount of calculations. As a simple but typical example, it demonstrates the strength and the great potential of the two-step homotopy perturbation transform method to solve nonlinea...

In this paper, we studied the numerical solution of nonlinear weakly singular Volterra-Fredholm integral equations by using the product integration method. Also, we shall study the convergence behavior of a fully discrete version of a product integration method for numerical solution of the nonlinear Volterra-Fredholm integral equations. The reliability and efficiency of the proposed scheme are...

In this work we consider a certain class of Volterra integral equations possessing an infinite set of solutions. We investigate the application of Euler’s method together with the use of extrapolation procedures. Several examples are considered illustrating our results as well as the use of graded meshes and the application of higher order methods. keywords Volterra integral equations; weakly s...