In this paper, we consider problems of discrete approximation special integral operators with the Calderon–Zygmund kernel. We introduce spaces and bounded acting in these spaces; then use for search approximate solutions corresponding equations. state theorems on solvability equations operators, compare their analogs, obtain estimates errors solutions.

in this paper, we introduce an efficient method for solving the quadratic riccati differential equation. in this technique, combination of laplace transform and new homotopy perturbation methods (ltnhpm) are considered as an algorithm to the exact solution of the nonlinear riccati equation. unlike the previous approach for this problem, so-called nhpm, the present method, does not need the init...

This paper successfully applies the Adomian decomposition  and the modified Laplace Adomian decomposition methods to find  the approximate solution of a nonlinear fractional Volterra-Fredholm integro-differential equation. The reliability of the methods and reduction in the size of the computational work give these methods a wider applicability. Also, the behavior of the solution can be formall...

Gradecast is a simple three-round algorithm presented by Feldman and Micali. The current work presents a very simple synchronous algorithm that utilized Gradecast to achieve Byzantine agreement. Two small variations of the presented algorithm lead to improved algorithms for solving the Approximate agreement problem and the Multi-consensus problem. An optimal approximate agreement algorithm was ...