Explicit hybrid six-step, sixth order, fully symmetric methods for solving y '' = f (x,y)

摘要

A family of explicit, fully symmetric, sixth order, six-step methods for the numerical solution of y '' = f(x,y) is studied. This family wastes two function evaluations per step and can be derived through interpolation techniques. An interval of periodicity is possessed and the phase lag is of high order. Numerical instabilities usually present in such type of multistep methods were circumvented. We conclude with extended numerical tests over a set of problems justifying our effort of dealing with the new methods.