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

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Abstract

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)7FEq1 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 approach is more efficient compared with the well known Runge-Kutta Dormand-Prince RK5(4)7S method [see Dormand and Prince (1980)] and the well known Runge-Kutta RK5(4)7FEq1 method of Higham and Hall (1990).

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  1. Section of Mathematics, Department of Civil Engineering, School of Engineering, Democritus University of Thrace, GR-671 00, Xanthi, Greece

    T. E. Simos

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Simos, T.E. Some Modified Runge-Kutta Methods for the Numerical Solution of Initial-Value Problems with Oscillating Solutions. Journal of Scientific Computing 13, 51–63 (1998). https://doi.org/10.1023/A:1023204727185

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  • DOI: https://doi.org/10.1023/A:1023204727185

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