A Parallel ODE Solver Adapted to Oscillatory Problems

Abstract

We propose a multistep method for solving special second-order ordinary differential equations with damped oscillatory solutions. The proposed methods integrate exactly (with only round-off error) ordinary polynomials and the product of trigonometric functions at a frequency ω by exponentials of a parameter g. When ωege0 they reduce to the classical Nystron and Cowell methods. Although there exist several methods with these properties, the proposed method allows independent computation of predictor and corrector which motivates parallel implementation.