Line Integral solution of Hamiltonian PDEs

Abstract

In this paper, we report about 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.

33 pages, 3 figures, 3 tables

References in corpus (5)

• Spectrally accurate space-time solution of Hamiltonian PDEs
• On the effectiveness of spectral methods for the numerical solution of multi-frequency highly-oscillatory Hamiltonian problems
• Analysis of Energy and QUadratic Invariant Preserving (EQUIP) methods
• Analysis of Spectral Hamiltonian Boundary Value Methods (SHBVMs) for the numerical solution of ODE problems
• Line Integral Solution of Hamiltonian Systems with Holonomic Constraints

Cited by in corpus (5)

• Arbitrarily high-order energy-preserving methods for simulating the gyrocenter dynamics of charged particles
• Analysis of Spectral Hamiltonian Boundary Value Methods (SHBVMs) for the numerical solution of ODE problems
• A note on the continuous-stage Runge-Kutta-(Nyström) formulation of Hamiltonian Boundary Value Methods (HBVMs)
• Spectrally accurate space-time solution of Manakov systems
• Continuous-Stage Runge-Kutta approximation to Differential Problems