In the research, special type of linear volterra integro-differential equations is considered. This paper compares the Homotopy perturbation method (HPM) with finite difference method for solving these equations. HPM is an analytical procedure for finding the solutions of problems which is based on the constructing a Homotopy with an imbedding parameter p that is considered as a small parameter...

In this note we prove the stochastic homogenization for a large class of fully nonlinear elliptic integro-differential equations in stationary ergodic random environments. Such equations include, but are not limited to Bellman equations and the Isaacs equations for the control and differential games of some pure jump processes in a random, rapidly varying environment. The translation invariant ...

In this paper, we consider an implicit block backward differentiation formula (BBDF) for solving Volterra Integro-Differential Equations (VIDEs). The approach given in this paper leads to numerical methods for solving VIDEs which avoid the need for special starting procedures. Convergence order and linear stability properties of the methods are analyzed. Also, methods with extensive stability r...