Cheap one-step global error estimation for ODEs (Q2708036)

The authors propose one-step methods to integrate numerically the initial value problem for systems of the form NEWLINE\[NEWLINEdy/dx= f(y),\quad y\in\mathbb{R}^D,\quad y(t_0)= y_0.NEWLINE\]NEWLINE The proposed methods have the property that besides giving a numerical approximation of the solution, it yields simultaneously an estimate of the global error without supplementary work. Numerical experiments support the authors' assertion that the methods are comparable to well known one-step integrators.