Some Nyström pairs for the general second-order initial-value problem (Q1200174)

Second order equations \(y''=f(x,a,y')\) with the usual Cauchy conditions can be numerically solved by explicit Nyström methods. The formulas defining the Nyström method can be obtained in two ways: (i) Directly, by using the order defining equations or, (ii) via Runge-Kutta pairs. The authors consider especially pairs of order \((p-1,p)\) with \(p=4,5,6\) and discuss the efficiency, accuracy and local error estimates. Numerical examples illustrate the advantages and drawbacks of the two approaches.