Solution of Shiff Systems by Using Differential Transform Method (original) (raw)
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Application to differential transformation method for solving systems of differential equations
In this paper, we present an analytical solution for different systems of differential equations by using the differential transformation method. The convergence of this method has been discussed with some examples which are presented to show the ability of the method for linear and non-linear systems of differential equations. We begin by showing how the differential transformation method applies to a non-linear system of differential equations and give two examples to illustrate the sufficiency of the method for linear and non-linear stiff systems of differential equations. The results obtained are in good agreement with the exact solution and Runge-Kutta method. These results show that the technique introduced here is accurate and easy to apply.
Mathematics and Statistics, 2020
The method of differential transform (DTM) is among the famous mathematical approaches for obtaining the differential equations solutions. This is due to its simplicity and efficient numerical performance. However, the major drawback of the DTM is obtaining a truncated series solution which is often a good approximation to the true solution of the equation in a specified region. In this study, a modification of DMT scheme known as MDTM is proposed for obtaining an accurate approximation of ordinary differential equations of second order. The scheme whose procedure is designed via DTM, the Laplace transforms and finally Padé approximation, gives a good approximate for the true solution of the equations in a large region. The proposed approach would be able to overcome the difficulty encountered using the classical DTM, and thus, can serve as an alternative approach for obtaining the solutions of these problems. Preliminary results are presented based on some examples which illustrate the strength and application of the defined scheme. Also, all the obtained results corresponded to exact solutions.
A Review: Differential Transform Method for Semi-Analytical Solution of Differential Equations
International Journal of Applied Mechanics and Engineering, 2020
In this article, the semi-analytical method known as the Differential Transform Method (DTM) for solving different types of differential equations is reviewed. First, basic definitions and formulas of DTM and Differential Transform-Padé approximation (DTM-Padé), which are used to increase the convergence and accuracy of DTM approximations, are discussed. Then both techniques of DTM and DTM-Padé, which have been successfully applied to partial differential equations, as well as the application of these methods in fluid mechanic and heat transfer are presented. In addition, the extension of DTM for integral differential equations and the fuzzy differential transformation method (FDTM) for fuzzy problems are discussed.
A Cumulative Study on Differential Transform Method
International Journal of Mathematical, Engineering and Management Sciences, 2019
Many real-world phenomena when modelled as a differential equation don't generally have exact solutions, so their numerical or analytic solutions are sought after. Differential transform method (DTM) is one of the analytical methods that gives the solution in the form of a power series. In this paper, a cumulative study is done on DTM and its evolution as an effective method to solve the gamut of differential equations.
Applications of Differential Transform Method
promising to a broad class of linear and non-linear problems. The result of differential transform method is in good agreement with those obtained by using already existing ones. The differential transform method appeared to be effective, reliable, easy and flexible for finding the solutions for such type of initial value problems. DTM is an analytical & numerical method for solving a wide variety of numerical differential equations and usually gets the solution in series form.
Of the Differential-Algebraic Equations with Index 3 Using Differential Transform Method
2009
ÖZET Bu makalede, 3 indexli diferensiyel cebirsel denklemleri çözmek için diferensiyel transform yöntemini kullandık. İki farklı diferensiyel cebirsel denklem nümerik olarak çözüldü. Nümerik ve analitik çözümler karşılaştırıldı. Bu örnekler, diferensiyel transform yönteminin, diferensiyel cebirsel denklemlerin çözümü için uygun bir yöntem olduğunu gösterir. Çözümler için MAPLE bilgisayar cebiri programı kullanıldı.
Applications of Differential Transform Method To Initial Value Problems
ABSTRACT: In this article the Differential Transform method is employed for obtaining solutions for initial value problems. This method gives the series of solutions which can be easily converted to exact ones. The differential transform method was successfully applied to initial value problems. The findings of the study has demonstrated that the method is easy , effective and flexible. The results of the differential transform method is in good agreement with those obtained by using the already existing ones. The proposed method is promising to a broad class of linear and nonlinear problems.
Exact Solution for a Class of Stiff Systems by Differential Transform Method
Applied Mathematics, 2013
In this paper, Differential Transform Method (DTM) is proposed for the closed form solution of linear and non-linear stiff systems. First, we apply DTM to find the series solution which can be easily converted into exact solution. The method is described and illustrated with different examples and figures are plotted accordingly. The obtained result confirm that DTM is very easy, effective and convenient.
Application of Multi-Step Differential Transform Method
In this study, a reliable algorithm to develop approximate solutions for the problem of fluid flow over a stretching or shrinking sheet is proposed. It is depicted that the differential transform method (DTM) solutions are only valid for small values of the independent variable. The DTM solutions diverge for some differential equations that extremely have nonlinear behaviors or have boundary-conditions at infinity. For this reason the governing boundary-layer equations are solved by the Multi-step Differential Transform Method (MDTM). The main advantage of this method is that it can be applied directly to nonlinear differential equations without requiring linearization, discretization, or perturbation. It is a semi analytical-numerical technique that formulizes Taylor series in a very different manner. By applying the MDTM the interval of convergence for the series solution is increased. The MDTM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions for systems of differential equations. It is predicted that the MDTM can be applied to a wide range of engineering applications.