SOLUTION OF THE DIFFERENTIAL-ALGEBRAIC EQUATIONS WITH INDEX 3 USING DIFFERENTIAL TRANSFORM METHOD

Öz

In this paper, we have applied the differential transform method to solve differential-algebraic equations with index 3. Two kind of differential-algebraic equations have been considered and solved numerically, then we compared numerical and analytical solution of the given equations. Examples were presented to show the ability of the method for differential-algebraic equations. We have used MAPLE computer algebra system to solve given problems[4].

Anahtar Kelimeler

• Differential transform method,Differential-algebraic equation,Index of differential-algebraic equation,Power series

SOLUTION OF THE DIFFERENTIAL-ALGEBRAIC EQUATIONS WITH INDEX 3 USING DIFFERENTIAL TRANSFORM METHOD

Öz

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.

Anahtar Kelimeler

• Diferensiyel Transform Yöntemi,Diferensiyel-Cebirsel denklem,Diferensiyel-cebirsel denklemlerin indexi,Kuvvet serisi,MAPLE

Kaynakça

1. [1]J.K. Zhou, differential transformation and its Aplication for Electrcial Circuits, Huazhong University Pres,Wuhan, Chine, 1986.
2. [2]A. K. SEN, An Application of the Adomian Decomposition Method to the Transiet Bhavior of a Model Biochemical Reaction, J. Math. Anal. Appl. 131 (1986), 232-245.
3. [3]A. K. SEN, On the Time Course of the Reversible Michaelis–Menten Reaction, J. Theor. Biol. 135 (1988),483-493.
4. [4]G. Frank., MAPLE V:CRC Press Inc., 2000 Corporate Blvd., N.W., Boca Raton, Florida 33431, (1996).
5. [5]S.H. Ho, C.K. Chen, Analysis of general elastically end restrained non-uniform beams using differential transform, Appl. Math. Mod., 22, (1998), 219-234.
6. [6]C.K.Chen, S.H. Ho, Solving partial differential equations by two dimensional differential transform method, Applied Mathematics and Computation, 106, (1999), 171-179.
7. [7]M.J. Jang, C.L. Chen,Y.C. Liy, Two-dimonsional differential transform for partial differential equations, Applied Mathematics and Computation, 121, (2001), 261-270.
8. [8] I.H.Abdel-Halim Hassan, On solving same eigenvalue problems by using a differential transformation, Applied Mathematics and Computation, 127, (2002), 1-22.

9. [9]I.H.Abdel-Halim Hassan, Different applications for the differential transformation in the differential equations, Applied Mathematics and Computation, 129, (2002), 183-201.
10. [10]F.Ayaz, On the two-dimensional differential transform method, Applied Mathematics and Computation, 143, (2003), 361-374.
11. [11]F. Ayaz, Solutions of the systems of differential equations by differential transform method, Applied Mathematics and Computation, 147, (2004), 547-567.
12. [12]C. K Chen, S.P. Ju, Application of differential transformation to transient advective-dispersive transport equation, Applied Mathematics and Computation, 155, (2004), 25-38
13. [13]F. Ayaz, Applications of differential transform method to differential–algebraic equations, Applied Mathematics and Computation, 152, (2004), 649-657.
14. [14]A. Arikoglu, İ. Ozkol, Solution of differential-difference equations by using differential transform method, Applied Mathematics and Computation, 181, (2006), 153-162.
15. [15]H. Liu, Y. Song, Differential transform method applied to high index differential–algebraic equations, Applied Mathematics and Computation, 184, (2007), 748-753