A parametric symmetric linear four-step method for the efficient integration of the Schrodinger equation and related oscillatory problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:236

Article

Anastassi, Z. A.¹  Simos, T. E.^2,3 

[1] Sch Pedag & Technol Educ ASPETE, Dept Sci, GR-14121 Athens, Greece

[2] King Saud Univ, Dept Math, Coll Sci, Riyadh 11451, Saudi Arabia

[3] Univ Peloponnese, Fac Sci & Technol, Dept Comp Sci & Technol, Sci Computat Lab, GR-22100 Tripoli, Greece

关键词: Ordinary differential equations;    Numerical solution;    Finite difference methods;    Symmetric linear multistep methods;    Phase fitting;    Schrodinger equation;   

DOI  :  10.1016/j.cam.2012.03.016

来源: Elsevier

【 摘 要 】

In this article, we develop an explicit symmetric linear phase-fitted four-step method with a free coefficient as parameter. The parameter is used for the optimization of the method in order to solve efficiently the Schrodinger equation and related oscillatory problems. We evaluate the local truncation error and the interval of periodicity as functions of the parameter. We reveal a direct relationship between the periodicity interval and the local truncation error. We also measure the efficiency of the new method for a wide range of possible values of the parameter and compare it to other well known methods from the literature. The analysis and the numerical results help us to determine the optimal values of the parameter, which render the new method highly efficient. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free