In this paper, we apply the differential transformation method to high-order nonlinear VolterraFredholm integro-differential equations with separable kernels. Some different examples are considered the results of these examples indicated that the procedure of the differential transformation method is simple and effective, and could provide an accurate approximate solution or exact solution.

A sparse-grid method for solving multi-dimensional backward stochastic differential equations (BSDEs) based on a multi-step time discretization scheme [31] is presented. In the multi-dimensional spatial domain, i.e. the Brownian space, the conditional mathematical expectations derived from the original equation are approximated using sparse-grid Gauss-Hermite quadrature rule and (adaptive) hier...

to start with, having employed transformation wave, some nonlinear partial differential equations have been converted into an ode. then, using the infinite series method for equations with similar linear part, the researchers have earned the exact soliton solutions of the selected equations. it is required to state that the infinite series method is a well-organized method for obtaining exact s...

‎in this paper, we discuss about existence of solution forintegro-differential system and then we solve it  by using the petrov-galerkin method. in the petrov-galerkin method choosing the trial and test space is important, so  we use alpert multi-wavelet as basisfunctions for these spaces. orthonormality is one of theproperties of alpert multi-wavelet which helps us to reducecomputations in the...

This work presents an analytical solution of some nonlinear delay differential equations (DDEs) with variable delays. Such DDEs are difficult to treat numerically and cannot be solved by existing general purpose codes. A new method of steps combined with the differential transform method (DTM) is proposed as a powerful tool to solve these DDEs. This method reduces the DDEs to ordinary different...

The Euler-Lagrange equation plays an important role in the minimization problems of the calculus of variations. This paper employs the differential transformation method (DTM) for finding the solution of the Euler-Lagrange equation which arise from problems of calculus of variations. DTM provides an analytical solution in the form of an infinite power series with easily computable components. S...

In this study, the general partial differential equation of unsteady groundwater flow through non-homogeneous and anisotropic aquifer was solved by the fully implicit finite difference method with control volume approach. The calibration of permeability and storage coefficients as model parameters was performed by a transformation technique and application of Powell's non-linear optimization me...