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: Yanwei Zhang, Haitao Che, Yonglei Fang, Xiong You
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2013/937858
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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.
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publishDate 2013-01-01
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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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