High-accuracy P-stable Methods for y' = f(t, y)

We obtain a one-parameter family of sixth-order P-stable methodsfor the numerical integration of periodic or near-periodic differentialequations that are defined by initial-value problems of theform: y^" = f(t, y), y(t₀)= y₀, y^'(t₀)= y^’₀. Our P-stablemethods are symmetric and involve three function evaluationsper step (periteration, in case f(t, y) is non-linear in y).For non-linear problems, starting values for the solution ofthe implicit equations by modified Newton's method are suggestedand illustrated by an example.