Line Integral Solution of Hamiltonian PDEs

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