Oscillatory Störmer-Cowell methods (Q1971853)

The authors study the numerical solution of initial-value problems for systems of ordinary differential equations of the \[ {d^2{\mathbf y}\over dt^2}={\mathbf f}({\mathbf y}),\quad {\mathbf y},{\mathbf f}({\mathbf y})\in\mathbb{R}^d,\quad t_0\leq t\leq t_{\text{end}}, \] where the components of the solution are known to be periodic with frequencies in a given nonnegative interval. The aim of the paper is to exploit this extra information, by using the so-called ``tuning'' techniques based on the least squares and minimax approximation.