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.File | Dimensione | Formato | |
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