A Parallel ODE Solver Adapted to Oscillatory Problems

Authors:
J. Vigo-Aguiar;L. M. Quintales
Affiliations:
Department of Applied Mathematics, University of Salamanca, E37008 Salamanca, Spain jvigo@usal.es;Department of Informatica, University of Salamanca, E37008 Salamanca, Spain lamq@usal.es
Venue:
The Journal of Supercomputing
Year:
2001

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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 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.