In this paper, we introduce the Petrov-Galerkin method for solution of stochastic Volterra integral equations. Here, we use continues Lagrange-type k-0 elements, since these elements have simple structure and via them, the solution of stochastic Volterra integral equation is reduced to algebraic equations. Also the error analysis of this method is done. In Comparison with other methods, this me...

in this paper, existence theorems for the fuzzy volterra-fredholm integral equations of mixed type (fvfiemt) involving fuzzy number valued mappings have been investigated. then, by using banach's contraction principle, sufficient conditions for the existence of a unique solution of fvfiemt are given. finally, illustrative examples are presented to validate the obtained results.

In this work we are concerned with the numerical solution of a nonlinear weakly singular Volterra integral equation with a nonsmooth solution. We investigate the application of product integration methods and a detailed analysis of the Trapezoidal method is given. In order to improve the numerical results we consider extrapolation procedures and collocation methods based on graded meshes. Sever...

A new method is proposed for the numerical solution of linear mixed Volterra-Fredholm integral equations in one space variable. The proposed numerical algorithm combines the trapezoidal rule, for the integration in time, with piecewise polynomial approximation, for the space discretization. We extend the method to nonlinear mixed Volterra-Fredholm integral equations. Finally, the method is test...

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 d...

Abstract. Optimal control problems of forward-backward stochastic Volterra integral equations (FBSVIEs, in short) with closed control regions are formulated and studied. Instead of using spike variation method as one may imagine, here we turn to treat the non-convexity of the control regions by borrowing some tools in set-valued analysis and adapting them into our stochastic control systems. A ...

in this paper the fixed point theorem of schauder is used to prove the existence of a continuous solution of the nonlinear fuzzy volterra integral equations. then using some conditions the uniqueness of the solution is investigated.

in this paper, a nonlinear volterra-fredholm integral equation of the first kind is solved by using the homotopy analysis method (ham). in this case, the first kind integral equation can be reduced to the second kind integral equation which can be solved by ham. the approximate solution of this equation is calculated in the form of a series which its components are computed easily. the accuracy...

We present a new temporal approximation scheme for the boundary integral formulation of time-dependent scattering problems which can be combined with either collocation or Galerkin approximation in space. It uses the backward-in-time framework introduced in [P. J. Davies and D. B. Duncan, Convolution Spline Approximations of Volterra Integral Equations, www.mathstat. strath.ac.uk/research/repor...

T The nonlinear and linear Volterra-Fredholm ordinary integral equations arise from various physical and biological models. The essential features of these models are of wide applicable. These models provide an important tool for modeling a numerous problems in engineering and science [6, 7]. Modelling of certain physical phenomena and engineering problems [8, 9, 10, 11, 12] leads to two-dimens...