Four step in phase predictor corrector method for periodic initial value problems

Abstract

In this paper, 4-step in phase and with minimal phase-lag predictor-corrector methods are developed for the numerical integration of periodic initial value problems using the implicit method of Raptis-Simos [23]. The 4-step in phase P-C method is of order six and it possesses an interval of periodicity of size 3.3874. We also obtain a 4-step sixth-order P-C method with minimal phase-lag of order eight. The numerical results for ordinary and partial differential initial value problems show that the 4-step predictor-corrector in phase method gives accurate results comparable to those of the implicit in phase method of Raptis-Simos [23].