DAI Meng, YIN Xiaoyan. Unconditionally Optimal Error Estimates of the Semi-Implicit BDF2-FEM for Cubic Schrödinger Equations[J]. Applied Mathematics and Mechanics, 2019, 40(6): 663-681. doi: 10.21656/1000-0887.390209
Citation: DAI Meng, YIN Xiaoyan. Unconditionally Optimal Error Estimates of the Semi-Implicit BDF2-FEM for Cubic Schrödinger Equations[J]. Applied Mathematics and Mechanics, 2019, 40(6): 663-681. doi: 10.21656/1000-0887.390209

Unconditionally Optimal Error Estimates of the Semi-Implicit BDF2-FEM for Cubic Schrödinger Equations

doi: 10.21656/1000-0887.390209
Funds:  The National Natural Science Foundation of China(General Program)(11771259)
  • Received Date: 2018-07-31
  • Rev Recd Date: 2019-04-13
  • Publish Date: 2019-06-01
  • The optimal error estimates of the semi-implicit BDF2-FEM were studied for cubic Schrödinger equations. First, an error estimate was divided into 2 parts: the temporal-discretization and the spatial-discretization. Through introduction of a temporal-discretization equation, the uniform boundedness of the solution and the temporal error estimate were obtained. The unconditionally optimal error estimates of the 2nd-order backward difference (BDF2-FEM) semi-implicit scheme for cubic Schrdinger equations were given. Finally, numerical examples verify the theoretical analysis.
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