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On the finite‐differences schemes for the numerical solution of two dimensional Schrödinger equation
Author(s) -
Subaşi Murat
Publication year - 2002
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.10029
Subject(s) - mathematics , partial differential equation , partial derivative , alternating direction implicit method , scheme (mathematics) , finite difference scheme , finite difference , explicit and implicit methods , finite difference method , order (exchange) , schrödinger equation , mathematical analysis , first order partial differential equation , exact differential equation , finance , economics
In this study three different finite‐differences schemes are presented for numerical solution of two‐dimensional Schrödinger equation. The finite difference schemes developed for this purpose are based on the (1, 5) fully explicit scheme, and the (5, 5) Noye‐Hayman fully implicit technique, and the (3, 3) Peaceman and Rachford alternating direction implicit (ADI) formula. These schemes are second order accurate. The results of numerical experiments are presented, and CPU times needed for this problem are reported. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 752–758, 2002; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/num.10029.