Superstable two-step methods for the numerical integration of general second order initial value problems

摘要

For the numerical integration of general second order initial value problems y″ = f(t, y, y′), y(t0) = y0, y′(t0) = y′0, we report a new family of two-step fourth order methods which are superstable for the test equation: y″ + 2αy′ + β2y = 0, α, β ⩾ 0, α + β > 0. We also note a modification of the trapezoidal method which results in a superstable method.