Murat OSMAOĞLU, Muhammet KURULAY, Mustafa BAYRAM

SABiT KATSAYILI LiNEER DiFERENSiYEL CEBiRSEL DENKLEMLERiN DiFERENSiYEL DÖNÜŞÜM YÖNTEMİ İLE NÜMERİK ÇÖZÜMÜ

Bu cahsmada. miihendislik ve fen bilimleri alanindaki ~ogu modellemelerde ortaya cikan sabit katsayili lineer diferensiyel cebirsel denklem sistemlerinin cozulebilirligi arastmldi. Niimerik cozum icin diferensiyel donusurn metodu kullamldi. Bu metotIa denklem sistemlerinin yaklasik analitik cozumleri bulundu ve bu cozumler tam cozumlerle karsilastrıldı.

Anahtar Kelimeler:

Diferensiyel cebirsel denklem, cozulebilirlik, kuvvet serileri, index, diferensiyel donusum metodu

SABiT KATSAYILI LiNEER DiFERENSiYEL CEBiRSEL DENKLEMLERiN DiFERENSiYEL DÖNÜŞÜM YÖNTEMİ İLE NÜMERİK ÇÖZÜMÜ

In this study, we have investigated solvability of the linear differential-algebraic equations with constant coefficient which ocur in most of the modelles in engineering and physical sciences. Differential transform method has been used for numerical solution. We have obtained approximate analitical solution of the given equation systems using the method and compared numerical and analitycal solutions.

Keywords:

Diferensitial-algebraic equations, solvability, power series, index, differential transform method,

PDF

___

[1]. Arikoglu, A. ve Ozkol, I., "Solution of differential-difference equations by usmg differential transform method", Applied Mathematics and Computation, 181:153-162 (2006).
[2]. Ascher, U.M. ve Petzold, L.R ,"Projected implicit Runge-Kutta methods for differential-algebraic equations", SIAM, J. Numer. Anal., 28:1097-1120 (1991).
[3]. Ascher, U.M. ve Spiter, R.I., "Collocation software for boundary value differential-algebraic equations", SIAM, J. Sci. Comput., 15:938-952 (1994).
[4]. Ascher, U.M. ve Petzold, L.R, "Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations" ,Philadelphia, PA (1998).
[5]. Ascher, U.M. ve Petzold, L.R, "Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations" ,Philadelphia, PA (1998).
[6]. Ayaz, F., "On the two-dimensional differential transform method", Applied Mathematics and Computation, 143:361-374 (2003).
[7]. Ayaz, F., "Applications of differential transform method to differential-algebraic equations", Applied Mathematics and Computation, 152:649-657 (2004). .
[8]. Brenan, K.E., Campbell, S.L. ve Petzold, L.R, "Numerical Solution of Initial- Value,Problems in Differential-Algebraic Equations" , Elsevier, New York (1989).
[9]. Campbell, S.L. ve Gear, C.W., "The index of general nonlinear DAEs", Numer. Math. 72:173-196 (1995).
[10]. Celik, E. ve Bayram, M., "Arbitrary order numerical method for solving differential-algebraic equations by Pade series", Appl. Math. Comput., 137:57-65 (2003).
[11]. Celik, E. ve Bayram, M., "On the numerical solution of differential-algebraic equations by Pade series", Appl. Math. Comput. 137:151-160 (2003).
[12]. Celik, E. ve Bayram, M., "Numerical solution of differential-algebraic equation systems and applications", Appl. Math. Comput, 154:405-413 (2004).
[13]. Chen, C.K. ve Ho, S.H., "Solving partial differential equations by two-dimensional differential transform method", Applied Mathematics and Computation, 106:171-179 (1999).
[14]. Erturk, V.S., Momani, S. ve Odibat, Z., "Application of generalized differential transform method to multi-order fractional differential equations", Communications in Nonlinear Science and Numerical Simulation, In Pres (2007).
[15]. Gear, C.W. ve Petzold, L.R.,"ODE systems for the solution of differential-algebraic systems", SIAM, J. Numer. Anal., 21:716-728 (1984).
[16]. Guzel, N. ve Bayram, M., "On the numerical solution of differential-algebraic equations with index- 3", Applied Mathematics and Computations, 175:1320-1331 (2006).
[17]. Hairer, E., Lubich, C.H. ve Roche, M., "The Numerical Solution of Differential Algebraic Systems by Runge Kutta methods", Lecture Notes in Mathematics, Vol. 1409, Springer, Berlin (1989).
[18]. Hassan, LH., "On solving some eigenvalue problems by using a differential transformation", Applied Mathematics and Computation, 127:1-22 (2002).
[19]. Hosseini, M.M., "An index reduction method for linear Hessenberg systems", Applied Mathematics and Computation, 171:596-603 (2005).
[20]. Hosseini, M.M., "Adomian decomposition method for solution of differential algebraic equations", Journal Computational and Applied Mathematics, 197:495-501 (2006).
[21]. Hosseini, M.M., "Adomian decomposition method for solution of nonlinear differential algebraic equations", Applied Mathematics and Computation, 181:1737-1744 (2006).
[22]. Jang, MJ., Chen, c.L. ve Liy, L.C., "On solving the initial-value problems using the differential transformation method", Applied Mathematics and Computation, 115:145-160 (2000).
[23]. Jang, MJ., Chen,C.L. ve Liu,Y.C., "Two-dimensional differential transform for partial differential equations", Applied Mathematics and Computation, 121:261-270 (2001).
[24]. Koksal, M. ve Herdem, S., "Analysis of nonlinear circuits by using differential Taylor transform", Computers&Electrical Engineering, 28:513-525 (2002).
[25]. Liu, H. Ve Song, Y., "Differential transform method applied to high index differential-algebraic equations", Applied Mathematics and Computation, 184:748-753 (2007).
[26]. Marz, R, "The index of linear differential-algebraic equations with properly stated leading term",Results in Mathematics, 42:308-338 (2003).
[27]. Marz, R, "Solvability of linear differential-algebraic equations with properly stated leading terrn",Results in Mathematics, 45:88-105 (2004).
[28]. Petzold, L.R, "Differential-algebraic equations are not ODEs", SIAM, J. Sci. Statist. Comput, 3:367- 384 (1982).
[29]. Petzold, L.R, "Numerical solution of differential-algebraic equations, Theory and numerics of ordinary and partial differential equations", Clarendon Press, Oxford (1995).
[30]. Yang, X., Liu, Y. ve Bai, S., "A numerical solution of second-order linear partial differential equations by differential transform", Applied Mathematics and Computation, 173:792-802 (2006).
[31]. Zhou, J.K., "Differential Transformation and its Application for Electrical Circuits, Huazhong University Press, Wuhan", China (1986).