New Phase-Fitted and Amplification-Fitted Fourth-Order and Fifth-Order Runge-Kutta-Nyström Methods for Oscillatory Problems
نویسندگان
چکیده
منابع مشابه
A New Family of Phase-Fitted and Amplification-Fitted Runge-Kutta Type Methods for Oscillators
In order to solve initial value problems of differential equations with oscillatory solutions, this paper improves traditional Runge-Kutta RK methods by introducing frequency-depending weights in the update. New practical RK integrators are obtained with the phase-fitting and amplification-fitting conditions and algebraic order conditions. Two of the new methods have updates that are also phase...
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The construction of symmetric and symplectic exponentially-fitted Runge-Kutta methods for the numerical integration of Hamiltonian systems with oscillatory solutions is reconsidered. In previous papers fourth-order and sixth-order symplectic exponentially-fitted integrators of Gauss type, either with fixed or variable nodes, have been derived. In this paper new fourth-order integrators are cons...
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Fourth-order boundary value problems are solved by means of exponentially-fitted methods of different orders. These methods, which depend on a parameter, can be constructed following a six-step flow chart of Ixaru and Vanden Berghe. Special attention is paid to the expression of the error term and to the choice of the parameter in order to make the error as small as possible. Some numerical exa...
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Article history: Received 27 April 2010 Received in revised form 2 August 2010 Accepted 19 August 2010 Available online 26 August 2010
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ژورنال
عنوان ژورنال: Abstract and Applied Analysis
سال: 2013
ISSN: 1085-3375,1687-0409
DOI: 10.1155/2013/939367