A New Optimized Runge-Kutta Pair for the Numerical Solution of the Radial Schrödinger Equation
A new embedded pair of explicit modified Runge-Kutta (RK) methods for the numerical integration of the radial Schrödinger equation is presented. The two RK methods in the pair have algebraic orders five and four, respectively. The two methods of the embedded pair are derived by nullifying the phase...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/641236 |
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| _version_ | 1832562345586458624 |
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| author | Yonglei Fang Qinghong Li Qinghe Ming Kaimin Wang |
| author_facet | Yonglei Fang Qinghong Li Qinghe Ming Kaimin Wang |
| author_sort | Yonglei Fang |
| collection | DOAJ |
| description | A new embedded pair of explicit modified Runge-Kutta (RK) methods for the
numerical integration of the radial Schrödinger equation is presented. The two RK
methods in the pair have algebraic orders five and four, respectively. The two methods
of the embedded pair are derived by nullifying the phase lag, the first derivative of
the phase lag of the fifth-order method, and the phase lag of the fourth-order method. Nu
merical experiments show the efficiency and robustness of our new methods compared
with some well-known integrators in the literature. |
| format | Article |
| id | doaj-art-0df6e2e171dd4fd79bbc099986320614 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-0df6e2e171dd4fd79bbc0999863206142025-02-03T01:22:51ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/641236641236A New Optimized Runge-Kutta Pair for the Numerical Solution of the Radial Schrödinger EquationYonglei Fang0Qinghong Li1Qinghe Ming2Kaimin Wang3School of Mathematics and Statistics, Zaozhuang University, Zaozhuang 277160, ChinaDepartment of Mathematics, Chuzhou University, Chuzhou 239000, ChinaSchool of Mathematics and Statistics, Zaozhuang University, Zaozhuang 277160, ChinaSchool of Mathematics and Statistics, Zaozhuang University, Zaozhuang 277160, ChinaA new embedded pair of explicit modified Runge-Kutta (RK) methods for the numerical integration of the radial Schrödinger equation is presented. The two RK methods in the pair have algebraic orders five and four, respectively. The two methods of the embedded pair are derived by nullifying the phase lag, the first derivative of the phase lag of the fifth-order method, and the phase lag of the fourth-order method. Nu merical experiments show the efficiency and robustness of our new methods compared with some well-known integrators in the literature.http://dx.doi.org/10.1155/2012/641236 |
| spellingShingle | Yonglei Fang Qinghong Li Qinghe Ming Kaimin Wang A New Optimized Runge-Kutta Pair for the Numerical Solution of the Radial Schrödinger Equation Abstract and Applied Analysis |
| title | A New Optimized Runge-Kutta Pair for the Numerical Solution of the Radial Schrödinger Equation |
| title_full | A New Optimized Runge-Kutta Pair for the Numerical Solution of the Radial Schrödinger Equation |
| title_fullStr | A New Optimized Runge-Kutta Pair for the Numerical Solution of the Radial Schrödinger Equation |
| title_full_unstemmed | A New Optimized Runge-Kutta Pair for the Numerical Solution of the Radial Schrödinger Equation |
| title_short | A New Optimized Runge-Kutta Pair for the Numerical Solution of the Radial Schrödinger Equation |
| title_sort | new optimized runge kutta pair for the numerical solution of the radial schrodinger equation |
| url | http://dx.doi.org/10.1155/2012/641236 |
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