Solution of Eighth Order Boundary Value Problems Using Differential Transformation Technique (original) (raw)
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International Journal of Mathematics Trends and Technology, 2018
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.
Numerical solution of special 12th-order boundary value problems using differential transform method
Communications in Nonlinear Science and Numerical Simulation, 2009
In this paper, a differential transform method (DTM) is used to find the numerical solution of a special 12th-order boundary value problems with two point boundary conditions. The analysis is accompanied by testing differential transform method both on linear and nonlinear problems from the literature [Wazwaz AM. Approximate solutions to boundary value problems of higher-order by the modified decomposition method. Comput Math Appl 2000:40;679-91; Siddiqi SS, Ghazala Akram. Solutions of 12th order boundary value problems using non-polynomial spline technique. Appl Math Comput 2007. Twizell EH. Spline solutions of linear 12th-order boundary value problems. J Comput Appl Math 1997;78:371-90]. Numerical experiments and comparison with existing methods are performed to demonstrate reliability and efficiency of the proposed method.
Solving Linear and Non-Linear Eight Order Boundary Value Problems by Three Numerical Methods
Three numerical methods were implemented for solving the eight-order boundary value problems. These methods are Differential transformation method, Homotopy perturbation method, and Rung-Kutta of 4th Order method. Two physical problems from the literature were solved by these methods for comparing results. Solutions were presented in Tables and figures. The differential transformation method shows an effective numerical solution to linear boundary value problems. This considers an important contribution in solving boundary value problems by the differential transformation method.
The Use of Differential Transformations for Solving Non-Linear Boundary Value Problems
Proceedings of the National Aviation University, 2016
The aim of our study is comparison of method applications based on differential transformations for solving boundary value problems which are described by non-linear ordinary differential equations. Methods: This article reviews two approaches based on differential transformations for solving non-linear boundary value problems: the modified differential transform method and the system-analogue simulation method. Results: In this paper, we present results of the numerical solution of non-linear boundary value problem by methods based on differential transformations for demonstration the effectiveness and applicability of techniques. The relative error for given solutions, obtained with using first 6 discretes of differential spectra is presented. Discussion: Comparison of numerical solutions obtained by modified differential transform method and system-analogue simulation method with exact solution shows that both methods have good agreement with exact solution of non-linear boundary value problem for small intervals. However, application of system-analogue simulation method is preferential for big intervals, on which the boundary value problem is solved.
Numerical Solution of Two-Point Boundary ValueProblems via Differential Transform Method
2015
This paper considers the solution of two-point boundary value problems by the application of Differential Transform method. Two examples are solved to illustrate the technique and the results are compared with the exact solutions. The numerical results obtained show strong agreement with their corresponding exact solutions, and as such demonstrate reliability and great accuracy of the method
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.
2017
In this paper we present zhou's method (DTM) for solving the initial value problems involving fifth order ordinary differential equations initial value problems involving fifth order ordinary differential equations we introduce the concept of DTM & applied it to obtain solution of three numerical examples for demonstration. The results are compared with exact solution & DTM method results. There results show that the technique introduced here is accurate & easy to apply. KEYWORDS :-Ordinary differential equitationszhou's Method (DTM), Initial value problem 1.0 Introduction :-The purpose of this paper is to employ the DTM method on examples of ordinary differential equation of fifth order and compared with result obtain by exact solution by using complimentary function & particular integral. In recent years, Bizar J. used for Riccati differential equation(1), Opanuga On numerical solution of systems of ordinary differential equitations by numeriacla analytical method (2), Che...
In this paper, differential transformation method is applied to construct analytic solutions of the boundary value problems for linear and nonlinear 4 th order non-homogenous differential equations. The differential transformation method is tested using three physical model problems. Results are presented in tables and figures. It was appeared in comparing results of the differential transformation method with Rung-Kutta , and RK-Butcher solutions that the differential transformation method is more reliable and effective in solving linear and non-linear differential equations.