Volume 48, Issue 1
Sixth-order Compact Extended Trapezoidal Rules for 2D Schrödinger Equation

Xiao-Hui Wu, Yujiang Wu, Jinyun Yuan, Raimundo J. B. de Sampaio & Yan-Tao Wang

J. Math. Study, 48 (2015), pp. 30-52.

Published online: 2015-03

Preview Full PDF 490 1558
Export citation
  • Abstract

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.

  • Keywords

Schrödinger equation BVMs ETRs compact scheme Richardson extrapolation

  • AMS Subject Headings

65M06 65M12 65M15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

lxh09@lzu.edu.cn (Xiao-Hui Wu)

myjaw@lzu.edu.cn (Yujiang Wu)

yuanjy@gmail.com (Jinyun Yuan)

raimundo.sampaio@pucpr.br (Raimundo J. B. de Sampaio)

wangyt07@lzu.edu.cn (Yan-Tao Wang)

  • BibTex
  • RIS
  • TXT
@Article{JMS-48-30, author = {Wu , Xiao-Hui and Wu , Yujiang and Yuan , Jinyun and J. 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 = {

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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v48n1.15.03}, url = {http://global-sci.org/intro/article_detail/jms/9908.html} }
TY - JOUR T1 - Sixth-order Compact Extended Trapezoidal Rules for 2D Schrödinger Equation AU - Wu , Xiao-Hui AU - Wu , Yujiang AU - Yuan , Jinyun AU - J. B. de Sampaio , Raimundo AU - Wang , Yan-Tao JO - Journal of Mathematical Study VL - 1 SP - 30 EP - 52 PY - 2015 DA - 2015/03 SN - 48 DO - http://dor.org/10.4208/jms.v48n1.15.03 UR - https://global-sci.org/intro/article_detail/jms/9908.html KW - Schrödinger equation KW - BVMs KW - ETRs KW - compact scheme KW - Richardson extrapolation AB -

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.

Xiao-Hui Wu, Yu-Jiang Wu, Jin-Yun Yuan, Raimundo J. B. de Sampaio & Yan-Tao Wang. (2019). Sixth-order Compact Extended Trapezoidal Rules for 2D Schrödinger Equation. Journal of Mathematical Study. 48 (1). 30-52. doi:10.4208/jms.v48n1.15.03
Copy to clipboard
The citation has been copied to your clipboard