A high-order accurate wavelet method for solving Schrödinger equations with general nonlinearity

2017 ◽  
Vol 39 (2) ◽  
pp. 275-290 ◽  
Author(s):  
Jiaqun Wang ◽  
Xiaojing Liu ◽  
Youhe Zhou
Keyword(s):  
High Order ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Wavelet Method ◽  
General Nonlinearity

The Conservative Splitting High-Order Compact Finite Difference Scheme for Two-Dimensional Schrödinger Equations

2017 ◽  
Vol 15 (01) ◽  
pp. 1750079
Author(s):  
Bo Wang ◽  
Dong Liang ◽  
Tongjun Sun
Keyword(s):  
Difference Scheme ◽  
Fourth Order ◽  
Two Dimensions ◽  
High Order ◽  
Optimal Error Estimate ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Two Dimensional ◽  
Time Step ◽  
Order Accuracy

In this paper, a new conservative and splitting fourth-order compact difference scheme is proposed and analyzed for solving two-dimensional linear Schrödinger equations. The proposed splitting high-order compact scheme in two dimensions has the excellent property that it preserves the conservations of charge and energy. We strictly prove that the scheme satisfies the charge and energy conservations and it is unconditionally stable. We also prove the optimal error estimate of fourth-order accuracy in spatial step and second-order accuracy in time step. The scheme can be easily implemented and extended to higher dimensional problems. Numerical examples are presented to confirm our theoretical results.

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