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Volume 14, Issue 2
Exponential Fitted Methods for the Numerical Solution of the Schrödinger Equation

T. E. Simos

J. Comp. Math., 14 (1996), pp. 120-134.

Published online: 1996-04

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  • Abstract

A new sixth-order Runge-Kutta type method is developed for the numerical integration of the radial Schrödinger equation and of the coupled differential equations of the Schrödinger type. The formula developed contains certain free parameters which allows it to be fitted automatically to exponential functions. We give a comparative error analysis with other sixth order exponentially fitted methods. The theoretical and numerical results indicate that the new method is more accurate than the other exponentially fitted methods.

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@Article{JCM-14-120, author = {T. E. Simos}, title = {Exponential Fitted Methods for the Numerical Solution of the Schrödinger Equation}, journal = {Journal of Computational Mathematics}, year = {1996}, volume = {14}, number = {2}, pages = {120--134}, abstract = {

A new sixth-order Runge-Kutta type method is developed for the numerical integration of the radial Schrödinger equation and of the coupled differential equations of the Schrödinger type. The formula developed contains certain free parameters which allows it to be fitted automatically to exponential functions. We give a comparative error analysis with other sixth order exponentially fitted methods. The theoretical and numerical results indicate that the new method is more accurate than the other exponentially fitted methods.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9224.html} }
TY - JOUR T1 - Exponential Fitted Methods for the Numerical Solution of the Schrödinger Equation AU - T. E. Simos JO - Journal of Computational Mathematics VL - 2 SP - 120 EP - 134 PY - 1996 DA - 1996/04 SN - 14 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9224.html KW - AB -

A new sixth-order Runge-Kutta type method is developed for the numerical integration of the radial Schrödinger equation and of the coupled differential equations of the Schrödinger type. The formula developed contains certain free parameters which allows it to be fitted automatically to exponential functions. We give a comparative error analysis with other sixth order exponentially fitted methods. The theoretical and numerical results indicate that the new method is more accurate than the other exponentially fitted methods.

T. E. Simos. (1996). Exponential Fitted Methods for the Numerical Solution of the Schrödinger Equation. Journal of Computational Mathematics. 14 (2). 120-134. doi:
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