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Solutions of Different Types of the linear and Non- linear Higher-Order Boundary Value Problems by Dif- ferential Transformation Method

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2009

Key Words:

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AMS Codes:

Abstract (2. Language): 
In [12], a numerical comparison between the differential transform method and Adomian decomposition method for solving fourth-order boundary value problems was presented. In this article, we use the differential transformation method (DTM) to solve the linear and non-linear higher-order boundary value problems (HOBVPs). The method proved to be very successful and powerful in computing such elements. The specific problems chosen for this purpose is that of the different types of higher order (e.g. fifth, sixth, ninth, tenth and twelfth ) boundary value problems. The differential transformation (DT) solutions are compared with the theoretical solution. It is shown that the solutions obtained from the technique have a very high degree of accuracy.
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REFERENCES

References: 

[1] R.P. Agarwal, Boundary-value problems for high ordinary differential equations, World
Scientific, Singapore, (1986).
[2] Aytac Arıko˘glu and ˙Ibrahim Özkol, Solution of boundary value problems for integrodifferential
equations by using differential transform method, Appllied Mathematics
and Computation, 168, (2005), 1145-1158.
REFERENCES 446
[3] F. Ayaz , Solution of the system of differential equations by differential transform
method, Appllied Mathematics and Computation, 147,(2004), 547-567.
[4] N. Bildik, A. Konuralp, F.O. Bek and S. Küçükarslan, Solution of different type of the
partial differential equation by differential transform method and Adomian’s decomposition
method, Appllied Mathematics and Computation,172,(2006), 551-567.
[5] K. Bor-Lih, Application of the differential transformation method to the solutions of the
free convection problem, Appllied Mathematics and Computation, 165, (2005), 63-79.
[6] K. Bor-Lih, Thermal boundary-layer problems in a semi-infinite flat plate by the differential
transformation method, Appllied Mathematics and Computation, 150, (2004),
303-320.
[7] C. K. Chen, S. H. Ho, Solving partial differential eqyation by differential transforma,
Appllied Mathematics and Computation, 106, (1999), 171-179.
[8] C. K. Chen, S. H. Ho, Application of diffrential transformation to eigenvalue problems,
Appllied Mathematics and Computation, 79, (1996), 173-188.
[9] C. L. Chen, Y. C. Liu, Solution of two point boundary value problems using the differential
transformation method, Journal of Optimization Theory and Applications , 99,
(1998), 23-35.
[10] M. M. Chawia and C. P. Katti, finite difference methods for two-point boundary value
problem involving higher order differential equations, BIT, 19, (1979), 27-33.
[11] [11] K. Djidjeli, E.H. Twizell and A. Boutayeb, Numerical methods for special nonlinear
boundary-value problems of order 2m, Journal of Computational and Applied Mathematics,
47, (1993), 35-45.
[12] V.S. Ertürk, S. Momani, Comparing numerical methods for solving fourth-order boundary
value problems, Appllied Mathematics and Computation, 188,2, (2007) 1963-1968.
[13] I. H. Abdel-Halim Hassan, Different applications for the differential transformation in
the differential equations, Appllied Mathematics and Computation, 129, (2002), 183-
201.
[14] I. H. Abdel-Halim Hassan, On solving some eigenvalue problems by using a differential
transformation, Appllied Mathematics and Computation, 127, (2002), 1-22.
REFERENCES 447
[15] I. H. Abdel-Halim Hassan, Diffrential transformation technique for solving higher-order
initial value problems, Appllied Mathematics and Computation, 154, (2004), 299-311.
[16] M. J. Jang , C. L. Chen, Y.C. Liu, On solving the initial value problems using the differential
transformation method, Appllied Mathematics and Computation, 115, (2000),
145-160.
[17] J. M. Jang and C. L. Chen, Analysis of the response of a strongly nonlinear damped
system using a differential transformation technique, Appllied Mathematics and Computation,
88, (1997), 137-151.
[18] M.Malik and H. H. Dang, Vibration analysis of continuous system by differential transformation,
Appllied Mathematics and Computation, 96, (1998), 17-26.
[19] A. M. Wazwaz, The numerical solution of sixth-order boundary value problems by the
modified decomposition method, Appllied Mathematics and Computation, 118, (2001),
311-325.
[20] A.M.Wazwaz, Approximate solution to boundary value problems of higher order by the
modified decomposition method, ComputerMathematics with Applications, 40, (2000),
679-691.
[21] A. M. Wazwaz, The numerical solution of fifth-order boundary value problems by the
decomposition method, ApplliedMathematics and Computation, 136, (2001), 259-270.
[22] Y.L.Yeh, M.J. Jang and C. Wang , Analyzing the free vibrations of a plate using finite
difference and differential transformation method, Appllied Mathematics and Computation,
178, 2, (2006), 493-501.
[23] J. K. Zhou, Differential transformation and its application for electrical circutits, Huarjung
University Press, Wuhahn, China, 1986, (in Chinese).

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