Power series solution of non-linear first order differential equation systems

Bu makalede, lineer olmayan adi diferansiyel denklemlerin çözümü için kuvvet serisini kullandık. Nümerik yoldan elde edilen sonuçlarla, teorik yoldan elde edilen sonuçlar karşılaştırıldı ve lineer olmayan differansiyel denklem sistemlerinde metodun etkinliğini göstermek için örnekler verildi. Nümerik hesaplamalarda MAPLE bilgisayar cebiri sistemleri kullanıldı (FRANK, 1996).

Lineer olmayan birinci mertebeden denklem sistemlerinin kuvvet serisiyle çözümü

In this paper, we use power series method to solve non-linear ordinary differential equations Theoretical considerations has been discussed and some examples were presented to show the ability of the method for non-linear systems of differential equations. We use MAPLE computer algebra systems for numerical calculations (FRANK, 1996).

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1.AMODIO P, MAZZIA F, Numerical solution of differential-algebraic equations and Computation of consistent initial/boundary conditions. Journal of Computational and Applied Mathematics. 87, 135-146,1997.
2.ASCHER U.M., PETZOLD L.R., Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations. Philadelphia: society for industrial and Applied Mathematics, 1998.
3.BRENAN K E, CAMPBELL S L, PETZOLD L R, Numerical solution of Initial-value problems in Differential-Algebraic Equations, North-Holland, Amsterdam, 1989.
4.CORLISS G, CHANG Y F, Solving Ordinary Differential Equations Using Taylor Series, ACM Trans. Math. Soft. 8,114-144,1982.
5.ÇELİK E, KARADUMAN E, BAYRAM M, Numerical Method to Solve Chemical Differential-Algebraic Equations. International Journal of Quantum Chemistry, 89(5), 447-451, 2002.
6.ÇELİK E, BAYRAM M, Arbitrary Order Numerical Method for Solving Differetial-Algebraic Equation by Pade Series. Applied Mathematics and Computational, 57-65, 2003.
7.FRANK G, MAPLE V:CRC Press Inc., 2000 Corporate Blvd., N.W., Boca Raton, Florida 33431, 1996.
8.HAIRER E, WANNER G, Solving Ordinary Differential Equations II: Stiff and Differential-Algebreis Problems, Springer-Verlag, 1991.
9.HENRICI P, Applied Computational Complex Analysis, Vol. 1, Chap. 1, John Wiely & Sons, New York, 1974.
10.HULL TE, ENRIGHT WH, FELLEN BM, SEDGWICK AE, Comparing numerical methods for ordinary differential equations, SIAM J, Numerical Anal. 9,603,1972.
11.PRESS WH, FLANNERY BP, TEUKOLSKY SA,VETTERLING WT, Numerical Recipes, Cambridge University Press, Cambridge, 1988.