A high-order nodal discontinuous Galerkin method for nonlinear fractional Schr\"{o}dinger type equations

DOI10.1016/J.CNSNS.2017.06.018arXiv1704.01484MaRDI QIDQ6285194

Publication date: 5 April 2017

Abstract: We propose a nodal discontinuous Galerkin method for solving the nonlinear Riesz space fractional Schr"{o}dinger equation and the strongly coupled nonlinear Riesz space fractional Schr"{o}dinger equations. These problems have been expressed as a system of low order differential/integral equations. Moreover, we prove, for both problems,

L^{2}

stability and optimal order of convergence

O (h^{N + 1})

, where

h

is space step size and

N

is polynomial degree. Finally, the performed numerical experiments confirm the optimal order of convergence.

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) NLS equations (nonlinear Schrödinger equations) (35Q55) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Fractional partial differential equations (35R11)

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