Recently, the efficient numerical solution of Hamiltonian problems has been tackled by defining the class of energy-conserving Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs). Their derivation relies on the expansion of the vector field along the Legendre orthonormal basis. Interestingly, this approach can be extended to cope with other orthonormal bases and, in particular, we here consider the case of the Chebyshev polynomial basis. The corresponding Runge-Kutta methods were previously obtained by Costabile and Napoli (Numer. Algo., 27, 119–130 2021). In this paper, the use of a different framework allows us to carry out a novel analysis of the methods also when they are used as spectral formulae in time, along with some generalizations of the methods.

(Spectral) Chebyshev collocation methods for solving differential equations / Pierluigi Amodio, Luigi Brugnano, Felice Iavernaro. - In: NUMERICAL ALGORITHMS. - ISSN 1017-1398. - STAMPA. - (2023), pp. 1-26. [10.1007/s11075-022-01482-w]

(Spectral) Chebyshev collocation methods for solving differential equations

Luigi Brugnano
;
2023

Abstract

Recently, the efficient numerical solution of Hamiltonian problems has been tackled by defining the class of energy-conserving Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs). Their derivation relies on the expansion of the vector field along the Legendre orthonormal basis. Interestingly, this approach can be extended to cope with other orthonormal bases and, in particular, we here consider the case of the Chebyshev polynomial basis. The corresponding Runge-Kutta methods were previously obtained by Costabile and Napoli (Numer. Algo., 27, 119–130 2021). In this paper, the use of a different framework allows us to carry out a novel analysis of the methods also when they are used as spectral formulae in time, along with some generalizations of the methods.
2023
1
26
Pierluigi Amodio, Luigi Brugnano, Felice Iavernaro
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1295719
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