A high-order nodal discontinuous Galerkin method for nonlinear fractional Schrodinger type equations

作者：Aboelenen Tarek^*

来源：Communications in Nonlinear Science & Numerical Simulation, 2018, 54: 428-452.

DOI：10.1016/j.cnsns.2017.06.018

• Nonlinear fractional Schrodinger equation
• Strongly coupled nonlinear fractional
• Schrodinger equations
• Nodal discontinuous Galerkin method
• Stability
• Error estimates

We propose a nodal discontinuous Galerkin method for solving the nonlinear Riesz space fractional Schrdinger equation and the strongly coupled nonlinear Riesz space fractional Schrdinger equations. These problems have been expressed as a system of low order dif-ferential/ 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.

• 出版日期2018-1