@Article{JMS-48-30,
author = {Liu , Xiao-HuiWu , YujiangYuan , JinyunJ. B. de Sampaio , Raimundo and Wang , Yan-Tao},
title = {Sixth-Order Compact Extended Trapezoidal Rules for 2D Schrödinger Equation},
journal = {Journal of Mathematical Study},
year = {2015},
volume = {48},
number = {1},
pages = {30--52},
abstract = {<p style="text-align: justify;">Based on high-order linear multistep methods (LMMs), we use the class
of extended trapezoidal rules (ETRs) to solve boundary value problems of ordinary
differential equations (ODEs), whose numerical solutions can be approximated by
boundary value methods (BVMs). Then we combine this technique with fourth-order
Padé compact approximation to discrete 2D Schrödinger equation. We propose a
scheme with sixth-order accuracy in time and fourth-order accuracy in space. It is
unconditionally stable due to the favourable property of BVMs and ETRs. Furthermore,
with Richardson extrapolation, we can increase the scheme to order 6 accuracy
both in time and space. Numerical results are presented to illustrate the accuracy of
our scheme.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v48n1.15.03},
url = {http://global-sci.org/intro/article_detail/jms/9908.html}
}