Line Integral Solution of Hamiltonian PDEs
Copyright policy )Line Integral Solution of Hamiltonian PDEs
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.
- Università degli studi di Salerno Italy
- University of Bari Aldo Moro Italy
- University of Kent United Kingdom
- University of Florence Italy
Korteweg–de Vries equation, Hamiltonian PDEs, Energy-conserving methods; Hamiltonian Boundary Value Methods; Hamiltonian PDEs; Hamiltonian problems; HBVMs; Korteweg-de Vries equation; Line integral methods; Nonlinear Schrödinger equation; Semilinear wave equation; Spectral methods, Numerical Analysis (math.NA), Hamiltonian problems, 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, 65P10, 65M70, 65M20, 65L05, 65L06, spectral methods, semilinear wave equation, QA297, QA1-939, FOS: Mathematics, energy-conserving methods, line integral methods, Mathematics - Numerical Analysis, nonlinear Schrödinger equation, Hamiltonian Boundary Value Methods, HBVMs, Mathematics
Korteweg–de Vries equation, Hamiltonian PDEs, Energy-conserving methods; Hamiltonian Boundary Value Methods; Hamiltonian PDEs; Hamiltonian problems; HBVMs; Korteweg-de Vries equation; Line integral methods; Nonlinear Schrödinger equation; Semilinear wave equation; Spectral methods, Numerical Analysis (math.NA), Hamiltonian problems, 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, 65P10, 65M70, 65M20, 65L05, 65L06, spectral methods, semilinear wave equation, QA297, QA1-939, FOS: Mathematics, energy-conserving methods, line integral methods, Mathematics - Numerical Analysis, nonlinear Schrödinger equation, Hamiltonian Boundary Value Methods, HBVMs, Mathematics
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