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Mathematics 2019, 7(3), 275; https://doi.org/10.3390/math7030275

Line Integral Solution of Hamiltonian PDEs

1
Dipartimento di Matematica e Informatica “U. Dini”, Università di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy
2
School of Mathematics, Statistics & Actuarial Science, University of Kent, Sibson Building, Parkwood Road, Canterbury CT2 7FS, UK
3
Dipartimento di Matematica, Università di Bari, Via Orabona 4, 70125 Bari, Italy
*
Author to whom correspondence should be addressed.
Received: 8 January 2019 / Revised: 8 March 2019 / Accepted: 12 March 2019 / Published: 18 March 2019
(This article belongs to the Special Issue Geometric Numerical Integration)
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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. View Full-Text
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 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
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Brugnano, L.; Frasca-Caccia, G.; Iavernaro, F. Line Integral Solution of Hamiltonian PDEs. Mathematics 2019, 7, 275.

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