Recently, the numerical solution of stiffly/highly oscillatory Hamiltonian problems has been attacked by using Hamiltonian boundary value methods (HBVMs) as spectral methods in time. While a theoretical analysis of this spectral approach has been only partially addressed, there is enough numerical evidence that it turns out to be very effective even when applied to a wider range of problems. Here, we fill this gap by providing a thorough convergence analysis of the methods and confirm the theoretical results with the aid of a few numerical tests.

Analysis of spectral Hamiltonian boundary value methods (SHBVMs) for the numerical solution of ODE problems

Amodio P.;Iavernaro F.
2019

Abstract

Recently, the numerical solution of stiffly/highly oscillatory Hamiltonian problems has been attacked by using Hamiltonian boundary value methods (HBVMs) as spectral methods in time. While a theoretical analysis of this spectral approach has been only partially addressed, there is enough numerical evidence that it turns out to be very effective even when applied to a wider range of problems. Here, we fill this gap by providing a thorough convergence analysis of the methods and confirm the theoretical results with the aid of a few numerical tests.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11586/248581
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