A General Scheme for Solving Systems of Linear First-Order Differential Equations Based on the Differential Transform Method (original) (raw)
Related papers
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.
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.
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.
Solution of differential–difference equations by using differential transform method
Applied Mathematics and Computation, 2006
In this work, we successfully extended differential transform method (DTM), by presenting and proving new theorems, to the solution of differential-difference equations (DDEs). Theorems are presented in the most general form to cover a wide range of DDEs, being linear or nonlinear and constant or variable coefficient. In order to show the power and the robustness of the method and to illustrate the pertinent features of related theorems, examples are presented.
Application Of The Differential Transform Method To Differential-Algebraic Equations With Index 2
2008
In this paper, we have used the differential transform method to solve differential-algebraic equations with index 2. Two kind of differentialalgebraic equations have been considered and solved numericaly, then we compared numerical and analytical solution of the given equations. Examples were presented to show the ability of the method for differentialalgebraic equations. We use MAPLE computer algebra system to solve given problems [4].
n this paper, we will compare the Differential Transform Method (DTM) and Taylor Series Method (TSM) applied to the solution of linear and nonlinear ordinary differential equations. The comparison shows that the Differential Transform Method is reliable, efficient and easy to use from computational point of view. Although the both of methods provide the solution in an infinite series, the Differential Transform Method provides a fast convergent series of easily computable components and eliminates heavy computational work needed by Taylor Series Method.
Discrete Dynamics in Nature and Society, 2015
We implement a relatively new analytic iterative technique to get approximate solutions of differential algebraic equations system based on generalized Taylor series formula. The solution methodology is based on generating the residual power series expansion solution in the form of a rapidly convergent series with easily computable components. The residual power series method (RPSM) can be used as an alternative scheme to obtain analytical approximate solution of different types of differential algebraic equations system applied in mathematics. Simulations and test problems were analyzed to demonstrate the procedure and confirm the performance of the proposed method, as well as to show its potentiality, generality, viability, and simplicity. The results reveal that the proposed method is very effective, straightforward, and convenient for solving different forms of such systems.