Optimization of solution stiff differential equations using MHAM and RSK methods
محورهای موضوعی : Non linear Programming
شادان صدیق بهزادی
1
(
گروه ریاضی دانشگاه آزاد اسلامی واحد قزوین
)
کلید واژه: Optimization, Stiff differential equations, Power series method, MHAM method, RSK method,
چکیده مقاله :
In this paper, a nonlinear stiff differential equation is solved by using the Rosenbrock iterative method, modified homotpy analysis method and power series method. The approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relations. Some numerical examples are studied to demonstrate the accuracy of the presented methods.
در این مقاله، یک معادله دیفرانسیل خام غیرخطی با استفاده از روش تکراری Rosenbrock، روش تحلیلی Homotype و روش سری قدرت حل شده است. حل تقریبی این معادله در قالب مجموعه ای محاسبه می شود که اجزای آن با استفاده از روابط بازگشتی محاسبه می شوند. برخی از نمونه های عددی برای نشان دادن دقت روش های ارائه شده مورد مطالعه قرار می گیرند.
Adomian, G. (1994). Solving frontier problems of physics: The decomposition methodkluwer. Boston, MA.
Behiry, S. H., Hashish, H., El-Kalla, I. L., & Elsaid, A. (2007). A new algorithm for the decomposition solution of nonlinear differential equations. Computers & Mathematics with Applications, 54(4), 459-466.
Corliss, G., & Chang, Y. F. (1982). Solving ordinary differential equations using Taylor series. ACM Transactions on Mathematical Software (TOMS), 8(2), 114-144.
Kaya, D. (2004). A reliable method for the numerical solution of the kinetics problems. Applied mathematics and computation, 156(1), 261-270.
Perturbation, B. (2003). Introduction to the Homotopy analysis method Chapman and Hall/CRC Press,Boca Raton.
Rèpaci, A. (1990). Nonlinear dynamical systems: on the accuracy of Adomian's decomposition method. Applied Mathematics Letters, 3(4), 35-39.
Rosenbrock, H. (1960). An automatic method for finding the greatest or least value of a function. The Computer Journal, 3(3), 175-184.
Schmitt, B. A., & Weiner, R. (2004). Parallel two-step W-methods with peer variables. SIAM Journal on Numerical Analysis, 42(1), 265-282.
Wahlbin, L. (1974). Error estimates for a Galerkin method for a class of model equations for long waves. Numerische Mathematik, 23(4), 289-303.
Wanner, G., & Hairer, E. (1996) Solving Ordinary Differential Equations II, Stiff and Differential-Algebraic Equations. Springer-Verlag, Berlin.
Zhao, J. J., Xu, Y., Dong, S. Y., & Liu, M. Z. (2005). Stability of the Rosenbrock methods for the neutral delay differential-algebraic equations. Applied mathematics and computation, 168(2), 1128-1144.
