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Line Integral Solution of Hamiltonian PDEs

Author

Listed:
  • 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)

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.

Suggested Citation

  • Luigi Brugnano & Gianluca Frasca-Caccia & Felice Iavernaro, 2019. "Line Integral Solution of Hamiltonian PDEs," Mathematics, MDPI, vol. 7(3), pages 1-28, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:275-:d:214934
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    References listed on IDEAS

    as
    1. Jiang, Chaolong & Sun, Jianqiang & Li, Haochen & Wang, Yifan, 2017. "A fourth-order AVF method for the numerical integration of sine-Gordon equation," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 144-158.
    2. Barletti, L. & Brugnano, L. & Frasca Caccia, G. & Iavernaro, F., 2018. "Energy-conserving methods for the nonlinear Schrödinger equation," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 3-18.
    3. Brugnano, L. & Frasca Caccia, G. & Iavernaro, F., 2015. "Energy conservation issues in the numerical solution of the semilinear wave equation," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 842-870.
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