POWER SERIES SOLUTION OF DIFFERENTIAL ALGEBRAIC EQUATION

Öz

Bu makalede, Lineer diferensiyel cebirsel denklernleri cozmek icin kuvvet serisi yontemi uygulandi. Bu yontem diferensiyel cebirsel denklemlerin numerik 90zmek icin bir keyfi mertebe verir.. Biz bu metodu test etmek icin bir ornek verdik ve elde ettigirniz sonuc ile analitik cozumtl karsilastirdik.

Anahtar Kelimeler

• Diferensiyel cebirsel denklem,keyfi mertebe,kuvvet serisi

POWER SERIES SOLUTION OF DIFFERENTIAL ALGEBRAIC EQUATION

Öz

In this paper, we apply the power series method to solve a linear differential algebraic equation. This method gives an arbitrary order for solving differential algebraic equation numerically. We have given an example to test the method and the result of the our method compared the exact solution of the given problem.

Anahtar Kelimeler

• Differential Algebraic Equation,Arbitrary Order,Power Series

Kaynakça

1. [1] Henrici, P., Applied Computational Complex Analysis, Vol.1, John Wiely&Sons, New York, Chap.l, (1974).
2. [2]. Corliss G. And Chang Y. F., Solving Ordinary Differential Equations Using Taylor Series, ACM Trans. Math. Soft., 114-144,(1982).
3. [3]. K. E. Brenan, S. L. Campbell, L.R. Petzold, Numerical solution of Initial-value problems in Differential-Algebraic Equations, North-Holland, Amsterdam (1989).
4. [4]. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, Springer-verlag, (1991).
5. [5]. Kurulay,M, Differential Algebraic Equations solving with power series, master thesis,
6. [6]. U.M. Ascher, L.R. Petzold, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations. Philadelphia: Society for Industrial and Applied Mathematics, (1998).
7. [7]. H. Hirayama, Arbitrary order and A-stable numerical method for solving algebraicordinary differential equation by power series. 2nd International Conference on:Mathematics and Computers in Physics. July9-16.(2ooo).
8. [8]. G.Frank., MAPLE V.CRC Press Inc., 2000 Corporate Blvd., N.W., Boca Raton, Florida33431, (1996).

9. [9] Weirning Wang, "An algorithm for solving DAEs with mechanization", Applied Mathematics and Computation, 67 1350-1372, (2005).
10. 10] Bayram, M.and Celik, E., "Arbitrary Order Numerical Method for Solving Differential-Algebraic Equations by Pade Series", Applied Mathematics and Computation. (2003),