In this paper we present a new approach for linear Volterra integral equations that is based on optimal control theory. Some optimal control problems corresponding Volterra integral equation be introduced which we solve these problems by discretization methods and linear programming approaches. Finally, some examples are given to show the efficiency of approach. Index Terms —Volterra integral e...

Abstract In this paper we first establish the existence, uniqueness and Hölder continuity of solution to stochastic Volterra integral equations (SVIEs) with weakly singular kernels, singularities $\alpha \in (0, 1)$ for drift term $\beta 1/2)$ term. Subsequently, propose a $\theta $-Euler–Maruyama scheme Milstein solve numerically obtain strong rates convergence both schemes in $L^{p}$ norm any...

In this paper, a Jacobi-collocation spectral method is developed for Volterra integral equations of second kind with a weakly singular kernel. We use some function transformation and variable transformations to change the equation into a new Volterra integral equation defined on the standard interval [−1, 1], so that the solution of the new equation possesses better regularity and the Jacobi or...

alternative legendre polynomials (alps) are used to approximate the solution of a class of nonlinear volterra-hammerstein integral equations. for this purpose, the operational matrices of integration and the product for alps are derived. then, using the collocation method, the considered problem is reduced into a set of nonlinear algebraic equations. the error analysis of the method is given an...