A zero-dissipative Runge-Kutta-Nyström method with minimal phase-lag.

Senu, Norazak; Suleiman, Mohamed; Ismail, Fudziah; Othman, Mohamed

Displaying similar documents to “A zero-dissipative Runge-Kutta-Nyström method with minimal phase-lag.”

Zero Dissipative DIRKN Pairs of Order 5(4) for Solving Special Second Order IVPs

S. O. Imoni, M. N. O. Ikhile (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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For initial value problem (IVPs) in ordinary second order differential equations of the special form $y^{''} = f (x, y)$ possessing oscillating solutions, diagonally implicit Runge–Kutta–Nystrom (DIRKN) formula-pairs of orders 5(4) in 5-stages are derived in this paper. The method is zero dissipative, thus it possesses a non-empty interval of periodicity. Some numerical results are presented to show the applicability of the new method compared with existing Runge–Kutta (RK) method applied to the problem...

High order explicit Runge-Kutta pairs for ephemerides of the solar system and the Moon.

Sharp, Philip W. (2000)

Journal of Applied Mathematics and Decision Sciences

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Nine-stage Multi-derivative Runge-Kutta method of order 12

Truong Nguyen-Ba, Vladan Božić, Emmanuel Kengne, Rémi Vaillancourt (2009)

Publications de l'Institut Mathématique

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On order 5 symplectic explicit Runge-Kutta Nyström methods.

Chou, Lin-Yi, Sharp, P.W. (2000)

Journal of Applied Mathematics and Decision Sciences

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Explicit two-step Runge-Kutta methods

Zdzisław Jackiewicz, Rosemary Anne Renaut, Marino Zennaro (1995)

Applications of Mathematics

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The explicit two-step Runge-Kutta (TSRK) formulas for the numerical solution of ordinary differential equations are analyzed. The order conditions are derived and the construction of such methods based on some simplifying assumptions is described. Order barriers are also presented. It turns out that for order $p \leq 5$ the minimal number of stages for explicit TSRK method of order $p$ is equal to the minimal number of stages for explicit Runge-Kutta method of order $p - 1$ . Numerical results are presented...

On total truncation error estimation for the one-step method

Anna Valková (1987)

Aplikace matematiky

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In this paper the author establishes estimation of the total truncation error after $s$ steps in the fifth order Ruge-Kutta-Huťa formula for systems of differential equations. The approach is analogous to that used by Vejvoda for the estimation of the classical formulas of the Runge-Kutta type of the 4-th order.

Self-similar solutions for the two-dimensional Nernst-Planck-Debye system

Łukasz Paszkowski (2012)

Applicationes Mathematicae

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We investigate the two-component Nernst-Planck-Debye system by a numerical study of self-similar solutions using the Runge-Kutta method of order four and comparing the results obtained with the solutions of a one-component system. Properties of the solutions indicated by numerical simulations are proved and an existence result is established based on comparison arguments for singular ordinary differential equations.

Toward a two-step Runge-Kutta code for nonstiff differential systems

Zbigniew Bartoszewski, Zdzisław Jackiewicz (2001)

Applicationes Mathematicae

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Various issues related to the development of a new code for nonstiff differential equations are discussed. This code is based on two-step Runge-Kutta methods of order five and stage order five. Numerical experiments are presented which demonstrate that the new code is competitive with the Matlab ode45 program for all tolerances.