An embedded explicit Runge-Kutta-Nystrom method for solving oscillatory problems

Senu N; Suleiman M; Ismail F

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An embedded explicit Runge-Kutta-Nystrom method for solving oscillatory problems

机译：嵌入式显式Runge-Kutta-Nystrom方法解决振动问题

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A new pair of embedded explicit Runge-Kutta-Nystrom (RKN) methods is developed to integrate second-order differential equations of the form q '' = f(t, q) where the solution is oscillatory. The embedded formula has dispersion order eight and dissipation order seven for the fifth-order formula. The cost for this pair is four function evaluations at each step of integration. Numerical comparisons with several codes in the scientific literature such as RKN5(4)D, RKN5(4)B, RKN4(3)G and DOPRI5 show the efficiency of the new method developed.

机译：开发了一对新的嵌入式显式Runge-Kutta-Nystrom（RKN）方法，以集成形式为q''= f（t，q）的二阶微分方程，其中该解决方案具有振荡性。嵌入式公式的色阶为八阶，色散阶为七阶。该对的成本是在集成的每个步骤中进行四个功能评估。与科学文献中的几个代码（例如RKN5（4）D，RKN5（4）B，RKN4（3）G和DOPRI5）进行数值比较，证明了该新方法的有效性。

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《Physica Scripta: An International Journal for Experimental and Theoretical Physics》 |2009年第1期|共7页
作者
Senu N; Suleiman M; Ismail F;
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正文语种 eng
中图分类物理学;
关键词
INITIAL-VALUE-PROBLEMS; MINIMAL PHASE-LAG; NUMERICAL-INTEGRATION; FORMULAS;

机译：初值问题;最小相位滞后;数值积分;公式;

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1. An embedded explicit Runge-Kutta-Nystrom method for solving oscillatory problems [J] . Senu N, Suleiman M, Ismail F Physica Scripta: An International Journal for Experimental and Theoretical Physics . 2009,第1期

机译：嵌入式显式Runge-Kutta-Nystrom方法解决振动问题
2. Embedded explicit two-step Runge-Kutta-Nystrom for solving special second-order IVPs [J] . L. M. Ariffin, N. Senu, M. Suleiman, Applied mathematical sciences . 2014,第94期

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3. Construction of an optimized explicit Runge-Kutta-Nystrom method for the numerical solution of oscillatory initial value problems [J] . A.A. Kosti, Z.A. Anastassi, T.E. Simos Computers & mathematics with applications . 2011,第11期

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4. A New Fourth-Order Four Stage Explicit Trigonometrically-Fitted Runge-Kutta-Nystrom Method for Solving Periodic Problems [C] . Musa A. Demba, Norazak Senu, Fudziah Ismail International Conference on Mathematical Sciences and Statistics . 2016

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7. A 5(4) Embedded Pair of Explicit Trigonometrically-Fitted Runge–Kutta–Nyström Methods for the Numerical Solution of Oscillatory Initial Value Problems [O] . Musa Demba, Norazak Senu, Fudziah Ismail 2016

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8. Diagonally Implicit Runge-Kutta-Nystrom Methods for Oscillatory Problems [R] . Vanderhouwen, P. J., Sommeijer, B. P. 1987

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An embedded explicit Runge-Kutta-Nystrom method for solving oscillatory problems

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