Phase-lag analysis of explicit Nyström methods fory″=f(x,y)

Abstract

We examine phase-lag (frequency distortion) of the two-parameter familyM ₄(α₁, α₃) of fourth order explicit Nyström methods of [1] by applying these to the test equation:y″+λ ² y=0, λ>0. While the methodM ₄(1/6, 5/6) possessing the largest interval of periodicity of size 3.46 has a phase-lag of (1/4320)H (H ⁴=λh, h is the step-size), we show that there exist two fourth order methods ofM ₄(α₁, α₃) for which the phase-lag is minimal and of size (1/40320)H ⁶; interestingly, both methods also possess a sizable interval of periodicity of length 2.75 each.