Line Integral Solution of Hamiltonian PDEs

Luigi Brugnano, Gianluca Frasca-Caccia and Felice Iavernaro
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Luigi Brugnano: Dipartimento di Matematica e Informatica “U. Dini”, Università di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy
Gianluca Frasca-Caccia: School of Mathematics, Statistics & Actuarial Science, University of Kent, Sibson Building, Parkwood Road, Canterbury CT2 7FS, UK
Felice Iavernaro: Dipartimento di Matematica, Università di Bari, Via Orabona 4, 70125 Bari, Italy

Mathematics, 2019, vol. 7, issue 3, 1-28

Abstract: In this paper, we report on recent findings in the numerical solution of Hamiltonian Partial Differential Equations (PDEs) by using energy-conserving line integral methods in the Hamiltonian Boundary Value Methods (HBVMs) class. In particular, we consider the semilinear wave equation, the nonlinear Schrödinger equation, and the Korteweg–de Vries equation, to illustrate the main features of this novel approach.

Keywords: Hamiltonian problems; energy-conserving methods; Hamiltonian Boundary Value Methods; HBVMs; line integral methods; spectral methods; Hamiltonian PDEs; semilinear wave equation; nonlinear Schrödinger equation; Korteweg–de Vries equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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