Some Modified Runge-Kutta Methods for the Numerical Solution of Initial-Value Problems with Oscillating Solutions

@article{Simos1998SomeMR,
  title={Some Modified Runge-Kutta Methods for the Numerical Solution of Initial-Value Problems with Oscillating Solutions},
  author={Theodore E. Simos},
  journal={J. Sci. Comput.},
  year={1998},
  volume={13},
  pages={51-63}
}
Two new modified Runge-Kutta methods with minimal phase-lag are developed for the numerical solution of initial-value problems with oscillating solutions which can be analyzed to a system of first order ordinary differential equations. These methods are based on the well known Runge-Kutta RK5(4)7FEql method of Higham and Hall (1990) of order five. Also, based on the property of the phase-lag a new error control procedure is introduced. Numerical and theoretical results show that this new… CONTINUE READING
BETA

Citations

Publications citing this paper.
SHOWING 1-10 OF 46 CITATIONS, ESTIMATED 32% COVERAGE

146 Citations

0102030'99'03'08'13'18
Citations per Year
Semantic Scholar estimates that this publication has 146 citations based on the available data.

See our FAQ for additional information.

References

Publications referenced by this paper.
SHOWING 1-10 OF 25 REFERENCES

A family of embedded Runge-Kutta formula

  • J. R. Dormand, P. J. Prince
  • J. Comput. Appl. Math
  • 1980
Highly Influential
6 Excerpts

A one-step method for direct integration of structural dynamics equations, Int'l

  • L. Brusa, L. Nigro
  • J. Number. Methods Engrg
  • 1980
Highly Influential
3 Excerpts

Modified Runge - Kutta Fehlberg methods for periodic initial - value problems

  • T. E. Simos
  • Japan J . Indust . Appl . Math .
  • 1995

Modified Runge-Kutta Fehlberg methods for periodic initial-value problems, Japan

  • T. E. Simos
  • J. Indust. Appl. Math
  • 1995

Runge-Kutta interpolants with minimal phase-lag

  • T. E. Simos
  • Comput. Math. Appl
  • 1993
3 Excerpts

A low order embedded Runge-Kutta method for periodic initial-value problems

  • A. B. Sideridis, T. E. Simos
  • J. Comput. Appl. Math
  • 1992
1 Excerpt

A two-step method with phase-lag of order infinity for the numerical integration of second order periodic initial-value problems, Int'l

  • T. E. Simos
  • J. Comput. Math
  • 1991

A four - step phase fitted method for the numerical integration of second order initial - value problems

  • A. D. Raptis, T. E. Simos
  • 1990

A four-step phase fitted method for the numerical integration of second order initial-value problems, BIT

  • A. D. Raptis, T. E. Simos
  • 1990

Embedded Runge-Kutta formula with stable equilibrium states

  • D. J. Higham, G. Hall
  • J. Comput. Appl. Math
  • 1990
1 Excerpt

Similar Papers

Loading similar papers…