A New Trigonometrically Fitted Two-Derivative Runge-Kutta Method for the Numerical Solution of the Schrödinger Equation and Related Problems
A new trigonometrically fitted fifth-order two-derivative Runge-Kutta method with variable nodes is developed for the numerical solution of the radial Schrödinger equation and related oscillatory problems. Linear stability and phase properties of the new method are examined. Numerical results are re...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/937858 |
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| _version_ | 1850166739693731840 |
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| author | Yanwei Zhang Haitao Che Yonglei Fang Xiong You |
| author_facet | Yanwei Zhang Haitao Che Yonglei Fang Xiong You |
| author_sort | Yanwei Zhang |
| collection | DOAJ |
| description | A new trigonometrically fitted fifth-order two-derivative Runge-Kutta method with
variable nodes is developed for the numerical solution of the radial Schrödinger equation
and related oscillatory problems. Linear stability and phase properties of the new
method are examined. Numerical results are reported to show the robustness and competence
of the new method compared with some highly efficient methods in the recent
literature. |
| format | Article |
| id | doaj-art-de8d238da1e04e799e2ca937b2eb88d8 |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-de8d238da1e04e799e2ca937b2eb88d82025-08-20T02:21:21ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/937858937858A New Trigonometrically Fitted Two-Derivative Runge-Kutta Method for the Numerical Solution of the Schrödinger Equation and Related ProblemsYanwei Zhang0Haitao Che1Yonglei Fang2Xiong You3Department of Mathematics and Information Science, Zaozhuang University, Zaozhuang 277160, ChinaSchool of Mathematics and Information Science, Weifang University, Weifang, Shandong 261061, ChinaDepartment of Mathematics and Information Science, Zaozhuang University, Zaozhuang 277160, ChinaDepartment of Applied Mathematics, Nanjing Agricultural University, Nanjing 210095, ChinaA new trigonometrically fitted fifth-order two-derivative Runge-Kutta method with variable nodes is developed for the numerical solution of the radial Schrödinger equation and related oscillatory problems. Linear stability and phase properties of the new method are examined. Numerical results are reported to show the robustness and competence of the new method compared with some highly efficient methods in the recent literature.http://dx.doi.org/10.1155/2013/937858 |
| spellingShingle | Yanwei Zhang Haitao Che Yonglei Fang Xiong You A New Trigonometrically Fitted Two-Derivative Runge-Kutta Method for the Numerical Solution of the Schrödinger Equation and Related Problems Journal of Applied Mathematics |
| title | A New Trigonometrically Fitted Two-Derivative Runge-Kutta Method for the Numerical Solution of the Schrödinger Equation and Related Problems |
| title_full | A New Trigonometrically Fitted Two-Derivative Runge-Kutta Method for the Numerical Solution of the Schrödinger Equation and Related Problems |
| title_fullStr | A New Trigonometrically Fitted Two-Derivative Runge-Kutta Method for the Numerical Solution of the Schrödinger Equation and Related Problems |
| title_full_unstemmed | A New Trigonometrically Fitted Two-Derivative Runge-Kutta Method for the Numerical Solution of the Schrödinger Equation and Related Problems |
| title_short | A New Trigonometrically Fitted Two-Derivative Runge-Kutta Method for the Numerical Solution of the Schrödinger Equation and Related Problems |
| title_sort | new trigonometrically fitted two derivative runge kutta method for the numerical solution of the schrodinger equation and related problems |
| url | http://dx.doi.org/10.1155/2013/937858 |
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