TY - JOUR
T1 - The improved complex variable element-free Galerkin method for two-dimensional Schrödinger equation
AU - Zhang, L. W.
AU - Deng, Y. J.
AU - Liew, K. M.
AU - Cheng, Y. M.
PY - 2014/11
Y1 - 2014/11
N2 - A numerical study of two-dimensional Schrödinger equation is carried out using the improved complex variable element-free Galerkin (ICVEFG) method. The ICVEFG method involves employment of the improved complex variable moving least-squares (ICVMLS) in the element-free Galerkin (EFG) procedure for numerical approximation. The ICVMLS is used to construct trial functions for the two-dimensional Schrödinger equation in the form of one-dimensional basis function that effectively reduces the number of unknown coefficients. In this study, the applicability of the ICVEFG method is examined through a number of numerical example problems. Convergence studies are carried out for these example problems by varying the number of nodes to ascertain convergent results are achieved as the number of nodes increases. The stability and accuracy of the ICVEFG method are validated by comparing the computed results with the exact solutions.
AB - A numerical study of two-dimensional Schrödinger equation is carried out using the improved complex variable element-free Galerkin (ICVEFG) method. The ICVEFG method involves employment of the improved complex variable moving least-squares (ICVMLS) in the element-free Galerkin (EFG) procedure for numerical approximation. The ICVMLS is used to construct trial functions for the two-dimensional Schrödinger equation in the form of one-dimensional basis function that effectively reduces the number of unknown coefficients. In this study, the applicability of the ICVEFG method is examined through a number of numerical example problems. Convergence studies are carried out for these example problems by varying the number of nodes to ascertain convergent results are achieved as the number of nodes increases. The stability and accuracy of the ICVEFG method are validated by comparing the computed results with the exact solutions.
KW - Galerkin method
KW - Galerkin's procedure
KW - Improved complex variable element-free
KW - Unsteady Schrödinger equation
UR - http://www.scopus.com/inward/record.url?scp=84908465237&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84908465237&origin=recordpage
U2 - 10.1016/j.camwa.2014.07.024
DO - 10.1016/j.camwa.2014.07.024
M3 - 21_Publication in refereed journal
VL - 68
SP - 1093
EP - 1106
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
SN - 0898-1221
IS - 10
ER -