In the modeling of a large class of problems in science and engineering, the minimization of a functional is appeared. Finding the solution of these problems needs to solve the corresponding ordinary differential equations which are generally nonlinear. In recent years, differential transform method has been attracted a lot of attention of the researchers for solving nonlinear problems. This me...

We show that the differential transform is well known Taylor series (contrary to what authors claim) and method (DTM) Frobenius method, commonly used obtain exact or approximate solutions equations. The generalized (GTM) merely application of Padé approximants produced by method. argue particular differential-difference nonlinear equations are scarce utility because initial conditions not flexi...

Abstract In this paper, we focus on the two-dimensional linear Telegraph equation with some initial and boundary conditions. We transform the model of partial differential equation (PDE) into a system of first order, linear, ordinary differential equations (ODEs). Our method is based on finding a solution in the form of a polynomial in three variables Un(x, y, t) = ∑n i=0 ∑n j=0 ∑n k=0 U(i, j, ...

This study investigates the use of differential transform method (DTM) for integrating Rössler system fractional order. Preliminary studies integer-order system, with reference to other well-established integration methods, made it possible assess quality and determine optimal parameter values that should be used when a different dynamic characteristics. Bifurcation diagrams obtained show that,...

The dynamic analysis of the biomechanical model of the head load impact using the Differential Transform Method is presented in this paper. In many parts of the world, the problem of traumatic brain injuries (TBI) has led to neurodegenerative dementing disorders and diseases as a result of head load impact from sporting activities, accidents involving the head, etc. have serious effects on huma...

This paper presents a study using novel linearization technique based on the Differential transformation method (DTM) to seek analytical solutions if it exists and approximate where closed form are not available. The effectiveness accuracy of this procedure is verified by solving six problems comprising both initial boundary value combination DTM Laplace transform method. resulting solution the...

In the present research, free vibration and modal stress analyses of thin circular plates with arbitrary edge conditions, resting on two-parameter elastic foundations are investigated.  Both Pasternak and Winkler parameters are adopted to model the elastic foundation. The differential transform method (DTM) is used to solve the eigenvalue equation yielding the natural frequencies and mode shape...

differential transform method has been applied to solve many functional equations so far. in this article, we have used this method to solve wave-like equations. differential transform method is capable of reducing the size of computational work. exact solutions can also be achieved by the known forms of the series solutions. some examples are prepared to show theefficiency and simplicity of th...

In this work, we proposed a hybrid algorithm to approximate the solution of Conformable Fractional Fokker-Planck Equation (CFFPE). This comprises unification two methods named Wave Transformation Method (FWTM) and Differential Transform (DTM). The method is based on steps. first step reduce given CFPDEs corresponding Partial Equations (PDEs). Then, second solve obtained PDEs iteratively by usin...