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A New Optimized Symmetric Embedded Predictor- Corrector Method (EPCM) for Initial-Value Problems with Oscillatory Solutions |
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PP: 703-713 |
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Author(s) |
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G. A. Panopoulos,
T. E. Simos,
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Abstract |
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| In this work a new optimized symmetric eight-step embedded predictor-corrector method (EPCM) with minimal phase-lag
and algebraic order ten is presented. The method is based on the symmetric multistep method of Quinlan-Tremaine [1], with eight
steps and eighth algebraic order and is constructed to solve numerically IVPs with oscillatory solutions. We compare the new method
to some recently constructed optimized methods and other methods from the literature. We measure the efficiency of the methods and
conclude that the new optimized method with minimal phase-lag is noticeably most efficient of all the compared methods and for all
the problems solved including the two-dimensional Kepler problem and the radial Schršodinger equation. |
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