A new class of explicit two-step fourth order methods for y″ = f(t, y) with extended intervals of periodicity

摘要

We introduce a new class of explicit two-step fourth order methods for the numerical integration of second order initial value problems: y″ = f(t, y), y(t0) = y0, y′(t0) = y′0. We show the interesting result that a method of this family which is based on m + 2 evaluations of f when applied to the test equation: y′ = − λ2y, λ > 0, possesses an interval of periodicity of length very nearly 2((m + 1)(m + 3))12. We also note a class of explicit second order methods for which a method based on m + 1 evaluations of f possesses an interval of periodicity of length very nearly 2(m + 1).