On the Construction of Exponentially-Fitted Methods for the Numerical Solution of the Schrödinger Equation

Article type: Research Article

Authors: Konguetsof, A. | Simos, T.E.^{; *}

Affiliations: Section of Mathematics, Department of Civil Engineering, Democritus University of Thrace, GR-671 00 Xanthi, Greece

Correspondence: [*] Corresponding author. Please use the following address for all related correspondence: Dr. T.E. Simos, 26 Menelaou Street, Amfithea – Paleon Faliron, GR–175 64 Athens, GREECE. E-mail: [email protected]. This work was supported by the research committee of Democritus University of Thrace (TΣMEΔE Research Programs) under contract: K.E. 679.

Abstract: In this paper an exponentially-fitted method is presented for the numerical solution of the Schrödinger equation. Trigonometric fitting is also explained and applicated. We show that the results we obtain are better than the ones without the trigonometric fitting.

Keywords: Exponential fitting, trigonometric fitting, Schrodinger equation, scattering problems, oscillating solutions

DOI: 10.3233/JCM-2001-1107

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 1, no. 1, pp. 143-160, 2001