A Parallel ODE Solver Adapted to Oscillatory Problems

Abstract. We propose a multistep method for solving special second-order ordinary differential equa-tions 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 exponen-tials of a parameter g. When ω = g = 0 they reduce to the classical Nyströn 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