On global superconvergence of iterated collocation solutions to linear second-kind Volterra integral equations

Monte Carlo Simulation to Solve the Linear Volterra Integral Equations of The Second Kind

This paper is intended to provide a numerical algorithm based on random sampling for solving the linear Volterra integral equations of the second kind. This method is a Monte Carlo (MC) method based on the simulation of a continuous Markov chain. To illustrate the usefulness of this technique we apply it to a test problem. Numerical results are performed in order to show the efficiency and accu...

Numerical Solution of Fuzzy Linear Volterra Integral Equations of the Second Kind by Homotopy Analysis Method

The solving linear one-dimemsional Volterra integral equations of the second kind in reproducing kernel space

In this paper, to solve a linear one-dimensional Volterra  integral equation of the second kind. For this purpose using the equation form, we have defined a linear transformation and by using it's conjugate and reproducing kernel functions, we obtain a basis for the functions space.Then we obtain the solution of  integral equation in terms of the basis functions. The examples presented in this ...

Numerical method for non-linear fuzzy Volterra integral equations of the second kind

Continuous collocation approximations to solutions of first kind Volterra equations

In this paper we give necessary and sufficient conditions for convergence of continuous collocation approximations of solutions of first kind Volterra integral equations. The results close some longstanding gaps in the theory of polynomial spline collocation methods for such equations. The convergence analysis is based on a Runge-Kutta or ODE approach.