Half-implicit pseudo two-step RKN methods (Q1964661)

The methods in the title are generalizations of Runge-Kutta-Nyström (RKN) methods. They share with pseudo Runge-Kutta methods the dependence of the increment in a step, on stages computed in the previous step as well as on the current step. It is shown how to construct methods with high stage order, as well as high order. Various levels of implicitness are identified and example methods are given up to order 4. Zero stability is proved and some numerical tests are reported.