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

Authors:
Z. A. Anastassi;T. E. Simos
Affiliations:
Department of Sciences, School of Pedagogical & Technological Education (ASPETE), N. Heraklion, GR-14121 Athens, Greece;Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia and Laboratory of Computational Sciences, Department of Computer Science and Technol ...
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

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Abstract

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.