Exponentially fitted methods with a local energy conservation law

2022/02/01 by Dajana Conte, Conte, Dajana, Gianluca Frasca-Caccia +1
Mathematics · Computer Science · #Numerical methods for differential equations #Differential Equations and Numerical Methods #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2202.00283

Abstract

A new exponentially fitted version of the Discrete Variational Derivative method for the efficient solution of oscillatory complex Hamiltonian Partial Differential Equations is proposed. When applied to the nonlinear Schroedinger equation, the new scheme has discrete conservation laws of charge and energy. The new method is compared with other conservative schemes from the literature on a benchmark problem whose solution is an oscillatory breather wave.

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