Recent advances in the numerical solution of the Nonlinear Schrödinger Equation
Luigi Barletti, Luigi Brugnano, Gianmarco Gurioli, Felice Iavernaro
Abstract
In this review we collect some recent achievements in the accurate and efficient solution of the Nonlinear Schrödinger Equation (NLSE), with the preservation of its Hamiltonian structure. This is achieved by using the energy-conserving Runge–Kutta methods named Hamiltonian Boundary Value Methods (HBVMs) after a proper space semi-discretization. The main facts about HBVMs, along with their application for solving the given problem, are here recalled and explained in detail. In particular, their use as spectral methods in time, which allows efficiently solving the problems with spectral space–time accuracy.
Topics & Concepts
MathematicsNonlinear systemNonlinear Schrödinger equationNumerical analysisMathematical analysisApplied mathematicsSchrödinger equationQuantum mechanicsPhysicsNumerical methods for differential equationsElectromagnetic Simulation and Numerical MethodsModel Reduction and Neural Networks