Sixth-order superstable two-step methods for second-order initial-value problems

摘要

For the numerical integration of general second-order initial-value problems y″ = f(x, y, y′), y(x0) = y0, y′(x0) = y′0, we report a family of two-step sixth-order methods which are superstable for the test equation y″ + 2αy′ + β2y = 0, α, β ⩾ 0, α + β\s>0, in the sense of Chawla [1].