Analysis of Spectral Hamiltonian Boundary Value Methods (SHBVMs) for the numerical solution of ODE problems
For researchers in numerical ODEs, this fills a theoretical gap for an effective spectral method, though it is an incremental extension of existing HBVMs.
The paper provides a thorough convergence analysis of Spectral Hamiltonian Boundary Value Methods (SHBVMs) for stiff/oscillatory ODEs, confirming theoretical results with numerical tests.
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.