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 a suitable orthonormal basis. Interestingly, this approach can be extended to cope with more general differential problems. In this paper we sketch this fact, by considering some relevant examples.

A general framework for solving differential equations / L. Brugnano, F. Iavernaro. - In: ANNALI DELL'UNIVERSITÀ DI FERRARA. SEZIONE 7: SCIENZE MATEMATICHE. - ISSN 0430-3202. - STAMPA. - 68:(2022), pp. 243-258. [10.1007/s11565-022-00409-6]

A general framework for solving differential equations

L. Brugnano
;
2022

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 a suitable orthonormal basis. Interestingly, this approach can be extended to cope with more general differential problems. In this paper we sketch this fact, by considering some relevant examples.
2022
68
243
258
L. Brugnano, F. Iavernaro
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1272586
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