The construction of trigonometrically fitted two step hybrid methods for the numerical solution
of second-order initial value problems is considered. These methods are suitable for the …

Our new linear symmetric semi-embedded predictor–corrector method (SEPCM) presented
here is based on the multistep symmetric method of Quinlan and Tremaine (1990), with eight …

The Falkner method is a multistep scheme intended for the numerical solution of second-
order initial value problems where the first derivative does appear explicitly. In this paper, we …

A linear multistep method (LMM) with continuous coefficients is considered and directly
applied to solve second order initial value problems (IVPs). The continuous method is used …

The phase lag and its first derivative can all vanish when utilising a phase-fitting strategy.
Since the new method employs the highest possible algebraic order (AOR) while …

A phase-fitting, first and second derivatives phase-fitting method is produced. The new
algorithm is singularly P-Stable and belongs to the economic algorithms. The new method is …

An approach to phase-fitting is devised, which includes methods for fitting the phase-lag and
for fitting its first, second, and third derivatives. Singularly P-Stable, the novel system belongs …

The phase lag and its first, second, third, fourth, and fifth derivatives are all accounted for in a
phase-fitting method. The new system uses the fewest possible function evaluations per …

Methods for fitting the phase-lag and its first, second, third, and fourth derivatives are
incorporated into a phase-fitting strategy. The novel system is singularly P-stable and is a …

A phase-fitting and first derivative phase-fitting method is developed. The new scheme is
singularly P-Stable and belongs to the economic algorithms. The new method is symbolized …