@Article{JICS-13-311,
author = {ChenyiZhu and Huawei Zhao},
title = {A linearized compact finite difference scheme for Schrödinger- Poisson System},
journal = {Journal of Information and Computing Science},
year = {2018},
volume = {13},
number = {4},
pages = {311--320},
abstract = { In this paper, a novel high accurate and efficient finite difference scheme is proposed for solving 
the Schrödinger-Poisson System. Applying a local extrapolation technique in time to the nonlinear part  makes  
the  proposed  scheme  linearized  in  the  implementation. In  fact, at  each  time  step, only two tri-diagonal 
linear  systems  of  algebraic  equations  are  solved  by  using  Thomas  method.  Another  feature  of  the  proposed 
method  is  the  high  spatial  accuracy  on  account  of  adopting  the  compact  finite  difference  approximation  to 
discrete the system in space. Moreover, the proposed scheme  preserves  the  total  mass  in  discrete  sense. 
Under  certain  regularity  assumptions  of  the exact  solution, the  local  truncation  error  of  the  proposed  
scheme  is  analyzed  in  detail  by  using Taylor’s  expansion, and  consequently  the  optimal  error  estimates  
of  the  numerical  solutions  are established by using the standard energy method and a mathematical induction 
argument.  The  convergence  order  is  of  O(τ  2  +  h4)  in  the  discrete  L2-norm  and  L∞-norm,  respectively. 
Numerical  results  are  reported  to  measure  the  theoretical  analysis, which  shows  that  the  new scheme is 
accurate and efficient and it preserves well the total mass and energy. 
},
issn = {3080-180X},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jics/22440.html}
}