P-stable symmetric super-implicitmethods for periodic initial value problems
نویسندگان
چکیده
منابع مشابه
P-stable high-order super-implicit and Obrechkoff methods for periodic initial value problems
This paper discusses the numerical solution of periodic initial value problems. Two classes of methods are discussed, superimplicit and Obrechkoff. The advantage of Obrechkoff methods is that they are high-order one-step methods and thus will not require additional starting values. On the other hand they will require higher derivatives of the right-hand side. In cases when the right-hand side i...
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In this paper, we propose a modification of the second order method introduced in [Q. Li and X. Y. Wu, A two-step explicit $P$-stable method for solving second order initial value problems, textit{Appl. Math. Comput.} {138} (2003), no. 2-3, 435--442] for the numerical solution of IVPs for second order ODEs. The numerical results obtained by the new method for some...
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In this paper, we present an explicit one-step method for solving periodic initial value problems of second order ordinary differential equations. The method is P -stable, and of first algebraic order and high phase-lag order. To improve the algebraic order, we give a composition second order scheme with the proposed method and its adjoint. We report some numerical results to illustrate the eff...
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In this paper, we present a new two-step trigonometrically fitted symmetric Obrechkoff method. The method is based on the symmetric two-step Obrechkoff method, with eighth algebraic order, high phase-lag order and is constructed to solve IVPs with periodic solutions such as orbital problems. We compare the new method to some recently constructed optimized methods from the literature. The numeri...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2005
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2005.04.013