A class of two-step P-stable methods for the accurate integration of second order periodic initial value problems

The sixth order P-stable method with minimal phase lag for a second order initial-value problem

“…Definition 3. (Ananthakrishnaiah [3]) We define the phase lag of the method with stability polynomial (3) as the leading term in the expansion of…”

“…Cash [1], Chawla and Rao [2], Ananthakrishnaiah [3] developed sixth-order Pstable method with sixth order phase-lag. Thomas [4] developed sixth order almost P-stable formulae with eighth order phase lag.…”

𝑃-stable Obrechkoff methods with minimal phase-lag for periodic initial value problems

“…The minimal phase-lag method of Chawla and Rao [5] is of 0(h4) with interval of periodicity (0,2.71) whereas the method of Ananthakrishnaiah [1] is of 0(h2) and is P-stable. The derivations depend upon the definition for phase-lag error given by Brusa and Nigro [2].…”

“…Following Gladwell and Thomas [8], Chawla and Rao [5] and Ananthakrishnaiah [1] developed two-step methods with minimal phase-lag errors À6/i6/12096 and a6/j6/42000, respectively. The minimal phase-lag method of Chawla and Rao [5] is of 0(h4) with interval of periodicity (0,2.71) whereas the method of Ananthakrishnaiah [1] is of 0(h2) and is P-stable.…”