Solutions of different types of the linear and non-linear higher-order boundary value problems by differential transformation method

ERTÜRK, Vedat Suat; HASSAN, I. H. Abdel-Halim

Solutions of different types of the linear and non-linear higher-order boundary value problems by differential transformation method

I. H. Abdel-Halim HASSAN, (Department, of Mathematics, Faculty of Science, Zagazig Univercity, Zagazig, Egypt)

Vedat Suat ERTÜRK (Ondokuz Mayıs Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Samsun, Türkiye)

European Journal of Pure and Applied Mathematics (elektronik)

15 3

Yıl: 2009 Cilt: 2 Sayı: 3 Sayfa Aralığı: 426 - 447 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

Solutions of different types of the linear and non-linear higher-order boundary value problems by differential transformation method

Öz:

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.

Anahtar Kelime:

Konular: Matematik

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[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.
[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.
[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).

APA	HASSAN I, ERTÜRK V (2009). Solutions of different types of the linear and non-linear higher-order boundary value problems by differential transformation method. , 426 - 447.
Chicago	HASSAN I. H. Abdel-Halim,ERTÜRK Vedat Suat Solutions of different types of the linear and non-linear higher-order boundary value problems by differential transformation method. (2009): 426 - 447.
MLA	HASSAN I. H. Abdel-Halim,ERTÜRK Vedat Suat Solutions of different types of the linear and non-linear higher-order boundary value problems by differential transformation method. , 2009, ss.426 - 447.
AMA	HASSAN I,ERTÜRK V Solutions of different types of the linear and non-linear higher-order boundary value problems by differential transformation method. . 2009; 426 - 447.
Vancouver	HASSAN I,ERTÜRK V Solutions of different types of the linear and non-linear higher-order boundary value problems by differential transformation method. . 2009; 426 - 447.
IEEE	HASSAN I,ERTÜRK V "Solutions of different types of the linear and non-linear higher-order boundary value problems by differential transformation method." , ss.426 - 447, 2009.
ISNAD	HASSAN, I. H. Abdel-Halim - ERTÜRK, Vedat Suat. "Solutions of different types of the linear and non-linear higher-order boundary value problems by differential transformation method". (2009), 426-447.

APA	HASSAN I, ERTÜRK V (2009). Solutions of different types of the linear and non-linear higher-order boundary value problems by differential transformation method. European Journal of Pure and Applied Mathematics (elektronik), 2(3), 426 - 447.
Chicago	HASSAN I. H. Abdel-Halim,ERTÜRK Vedat Suat Solutions of different types of the linear and non-linear higher-order boundary value problems by differential transformation method. European Journal of Pure and Applied Mathematics (elektronik) 2, no.3 (2009): 426 - 447.
MLA	HASSAN I. H. Abdel-Halim,ERTÜRK Vedat Suat Solutions of different types of the linear and non-linear higher-order boundary value problems by differential transformation method. European Journal of Pure and Applied Mathematics (elektronik), vol.2, no.3, 2009, ss.426 - 447.
AMA	HASSAN I,ERTÜRK V Solutions of different types of the linear and non-linear higher-order boundary value problems by differential transformation method. European Journal of Pure and Applied Mathematics (elektronik). 2009; 2(3): 426 - 447.
Vancouver	HASSAN I,ERTÜRK V Solutions of different types of the linear and non-linear higher-order boundary value problems by differential transformation method. European Journal of Pure and Applied Mathematics (elektronik). 2009; 2(3): 426 - 447.
IEEE	HASSAN I,ERTÜRK V "Solutions of different types of the linear and non-linear higher-order boundary value problems by differential transformation method." European Journal of Pure and Applied Mathematics (elektronik), 2, ss.426 - 447, 2009.
ISNAD	HASSAN, I. H. Abdel-Halim - ERTÜRK, Vedat Suat. "Solutions of different types of the linear and non-linear higher-order boundary value problems by differential transformation method". European Journal of Pure and Applied Mathematics (elektronik) 2/3 (2009), 426-447.