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New phase fitted and amplification fitted Numerov-type methods for periodic IVPs with two frequencies. (English) Zbl 1253.65110
Summary: Phase fitted and amplification fitted Numerov-type methods for periodic initial value problems with two frequencies are investigated. A one-frequency method and a two-frequency method are constructed. The two new methods both have algebraic order five and are dispersive of order six and dissipative of order five. The two-dimensional absolute stability region for the one-frequency method and the three-dimensional absolute stability region for the two-frequency method are plotted. Numerical experiments are reported to show the efficiency and competence of the two new methods.

##### MSC:
 65L05 Initial value problems for ODE (numerical methods)
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##### References:
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