Exponentially fitted multi-derivative linear methods for the resonant state of the Schrödinger equation

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• 作者：Yanwei Zhang ; Xiong You ; Yonglei Fang
• 关键词：Exponentially fitted method ; Obrechkoff one ; step method ; Schrödinger equation ; Error analysis
• 刊名：Journal of Mathematical Chemistry
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：55
• 期：1
• 页码：223-237
• 全文大小：
• 刊物类别：Chemistry and Materials Science
• 刊物主题：Physical Chemistry; Theoretical and Computational Chemistry; Math. Applications in Chemistry;
• 出版者：Springer International Publishing
• ISSN：1572-8897
• 卷排序：55

文摘

A new family of exponentially fitted P-stable one-step linear methods involving several derivatives for the numerical integration of the Schrödinger equation are obtained. Numerical results are reported to show the efficiency and robustness of the new methods specially adapted to the integration of the radial time-independent Schrödinger equation for large energies. Error analysis is carried out and the asymptotic expressions of the local errors for large energies explain the results of the numerical experiments on the resonance problem.