New pairs of embedded Runge-Kutta methods specially adapted to the numerical solution of first order systems of differential equations which are assumed to possess oscillating solutions are obtained. These pairs have been derived taking into account not only the usual properties of accuracy, stabili
Some Modified Runge-Kutta Methods for the Numerical Solution of Initial-Value Problems with Oscillating Solutions
✍ Scribed by T. E. Simos
- Book ID
- 110432723
- Publisher
- Springer US
- Year
- 1998
- Tongue
- English
- Weight
- 468 KB
- Volume
- 13
- Category
- Article
- ISSN
- 0885-7474
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new approach for constructing efficient RungeKutta-Nystrom methods is introduced in this paper. Based on this new approach a new exponentially-fitted Runge-KuttaNystrGm fourth-algebraic-order method is obtained for the numerical solution of initial-value problems with oscillating solutions. The new
An exponentially-fitted Runge-Kutta method for the numerical integration of initial-value problems wi',h periodic or oscillating solutions is developed in this paper. Numerical and theoretical results obtained for several well known problems show the efficiency of the new method. (~
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