It is known that to construct the stable multistep method with the higher order of accuracy for solving integral equation is actual. For this aim here we suggest some ways for the construction of hybrid methods for solving nonlinear Volterra integral equations of the second kind. Thus, foundational this extends stable hybrid method with higher order of accuracy. Note that the hybrid methods whi...

In this paper, we conduct a comparative study between the homotopy perturbation method (HPM) and Adomian’s decomposition method (ADM) for analytic treatment of nonlinear Volterra integral equations, and we show that the HPM with a specific convex homotopy is equivalent to the ADM for these type of equations.

The paper presents an iterative numerical method for approximating solutions of two-dimensional Fredholm–Volterra integral equations the second kind. As these arise in many applications, there is a constant need accurate, but fast and simple to use approximations their solutions. proposed here uses successive Mann type suitable cubature formula. Mann’s procedure known converge faster than class...

In this study, we provide the Aboodh decomposition method, a novel analytical technique. The fundamental definitions and theorems of suggested approach are provided analyzed. This new method is mixture transform Adomian method. used to solve nonlinear integro-differential equations (IDEs), solutions given as quickly expanding series terms. We compute maximum absolute error some figures compare ...

In this work, we introduce a novel method for solving two-dimensional fuzzy Fredholm integral equations of the second kind (2D-FFIE-2). We use new representation of parametric form of fuzzy numbers and convert a two-dimensional fuzzy Fredholm integral equation to system of two-dimensional Fredholm integral equations of the second kind in crisp case. We can use Adomian decomposition method for n...

in this paper we investigate the existence and uniqueness for volterra-fredholm type integral equations and extension of this type of integral equations. the result is obtained by using the  coupled fixed point theorems in the framework of banach space $ x=c([a,b],mathbb{r})$. finally, we  give an example to illustrate the applications of our results.