New Runge–Kutta–Nyström formula-pairs of order 8(7), 9(8), 10(9) and 11(10) for differential equations of the form y″ = f(x, y)

摘要

For initial value problems in ordinary second-order differential equations of the special form y″ = f(x, y), mew explicit, direct Runge-Kutta-Nyström formula-pairs of order 8(7), 9(8), 10(9) and 11(10) are presented using the mode of Bettis, Dormand and Prince. Two numerical examples demonstrate the efficiency of the new formula-pairs.