New Phase Fitted and Amplification Fitted Numerov-Type Methods for Periodic IVPs with Two Frequencies

الملخص EN

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.