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arXiv · 1704.01484

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

Tarek Aboelenen
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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.

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Tarek Aboelenen. 2017-04-05. A high-order nodal discontinuous Galerkin method for nonlinear fractional Schr\"{o}dinger type equations. https://doi.org/10.1016/j.cnsns.2017.06.018

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