Line Integral solution of Hamiltonian PDEs
For researchers in numerical PDEs, this presents a novel energy-conserving method, but the paper is an incremental report without quantitative comparisons.
The paper applies energy-conserving line integral methods (HBVMs) to solve Hamiltonian PDEs, demonstrating the approach on the semilinear wave, nonlinear Schrödinger, and Korteweg-de Vries equations. No concrete numerical results are reported.
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.