In the course of this paper, the Optimal Homotopy Asymptotic Method (OHAM) introduced by Marica is applied to solve linear and nonlinear boundary value problems both for fourth-order integro-differential equations. The following analysis is accompanied by numerical examples whose results show that the Optimal Homotopy Asymptotic Method is highly accurate, convenient and relatively efficient for...

In the present study, we investigate the symmetry groups of Benney equations that are the system of nonlinear integro-differential equations. We first investigate the symmetry groups of the Benney equations by using the method. Then we obtain all reduced forms of the system of integro-differential equations with fewer variables based on symmetry groups; and lastly, we seek a similarity solution...

this paper investigates existence and uniqueness results for the first order fuzzy integro-differential equations. then numerical results and error bound based on the left rectangular quadrature rule, trapezoidal rule and a hybrid of them are obtained. finally an example is given to illustrate the performance of the methods.

Fuzzy integro-differential equations is one of the important parts of fuzzy analysis theory that holds theoretical as well as applicable values in analytical dynamics and so an appropriate computational algorithm to solve them is in essence. In this article, we use parametric forms of fuzzy numbers and suggest an applicable approach for solving nonlinear fuzzy integro-differential equations usi...

in this paper, first the properties of one and two-dimensional differential transforms are presented.next, by using the idea of differential transform, we will present a method to find an approximate solution fora volterra integro-partial differential equations. this method can be easily applied to many linear andnonlinear problems and is capable of reducing computational works. in some particu...

We review here various recent applications of Wassertein–type metrics to both nonlinear partial differential equations and integro–differential equations. Among others, we can describe the asymptotic behavior of nonlinear friction equations arising in the kinetic modelling of granular flows, and the growth of the support in nonlinear diffusion equations of porous medium type. Further examples i...

In this paper, the variational iteration method for solving nth-order fuzzy integro-differential equations (nth-FIDE) is proposed. In fact the problem is changed to the system of ordinary fuzzy integrodifferential equations and then fuzzy solution of nth-FIDE is obtained. Some examples show the efficiency of the proposed method.

Here a posteriori error estimate for the numerical solution of nonlinear Voltena- Hammerstein equations is given. We present an error upper bound for nonlinear Voltena-Hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of Brunner for these problems (the implicitly linear collocation method)...

In the present paper using homotopy analysis method (HAM), we approximate a special case of fuzzy integral equations. The fuzzy integral and integro-differential equations have a wide range of applications in science and engineering. In this paper HAM can be to find the exact solution or an approximate solution of the problem. Within this paper the HAM is used to obtain A series solution of int...