in this paper, we apply the differential transform (dt) method for finding approximate solution of the system of linear and nonlinear volterra integro-differential equations with variable coefficients, especially of higher order. we also obtain an error bound for the approximate solution. since, in this method the coefficients of taylor series expansion of solution is obtained by a recurrence r...

In this paper difference methods to solve "fuzzy partial differential equations" (FPDE) such as fuzzy hyperbolic and fuzzy parabolic equations are considered. The existence of the solution and stability of the method are examined in detail. Finally examples are presented to show that the Hausdorff  distance between the exact solution and approximate solution tends to zero.

This paper demonstrates a study on some significant latest innovations in the approximated techniques to find the approximate solutions of Caputo fractional Volterra-Fredholm integro-differential equations. To this aim, the study uses the modified Adomian decomposition method (MADM) and the modified variational iteration method (MVIM). A wider applicability of these techniques are based on thei...

This article presents a new iterative method (NIM) for the investigation of approximate solution Klein-Gordon and sine-Gordon equations. approach is formulated on combination Mohand transform homotopy perturbation method. (MT) capable to handle linear terms only, thus we introduce (HPM) tackle nonlinear terms. NIM derives results in form series solution. The proposed emphasizes stability derive...

We consider the backward error associated with a given approximate solution of a linear least squares problem. The backward error can be very expensive to compute, as it involves the minimal singular value of certain matrix that depends on the problem data and the approximate solution. An estimate based on a regularized projection of the residual vector has been proposed in the literature and a...

In this paper, the numerical technique based on hybrid Bernoulli and Block-Pulse functions has been developed to approximate the solution of system of linear Volterra integral equations. System of Volterra integral equations arose in many physical problems such as elastodynamic, quasi-static visco-elasticity and magneto-electro-elastic dynamic problems. These functions are formed by the hybridi...

In this paper, a new approach for finding an approximate solution for discrete optimal control problems is introduced. In this method the problem is transformed to a continuous optimal control problem whose solution may give rise to a good approximate solution for the original problem. Then, a measure-theoretical approach is applied to solve the new problem. The method is extended to solve time...

This paper presents a set of linearized equations was derived for the motion, relative to an elliptical reference orbit, of an object influenced by J2 perturbation terms. Approximate solution for simulations was used to compare these equations and the linearized keplerian equations to the exact equations. The inclusion of the linearized perturbations in the derived equations increased the high ...

We propose a new verification method to enclose solutions for initial value problems of systems of first-order nonlinear ordinary differential equations (ODEs) using a linearized inverse operator. The proposed approach can verify the existence and local uniqueness of the exact solution independent of the choice of the approximation scheme, while the existing methods usually depend on the numeri...