An economical eighth-order method for the approximation of the solution of the Schrödinger equation

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• 作者：Zhiwei Wang ; T. E. Simos
• 关键词：Phase ; lag ; Derivative of the phase ; lag ; Symmetric ; Multistep ; Schrödinger equation
• 刊名：Journal of Mathematical Chemistry
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：55
• 期：3
• 页码：717-733
• 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

In this paper we introduce, for the first time in the literature, a three-stages two-step method. The new algorithm has the following characteristics: (1) it is a two-step algorithm, (2) it is a symmetric method, (3) it is an eight-algebraic order method (i.e of high algebraic order), (4) it is a three-stages method, (5) the approximation of its first layer is done on the point \(x_{n-1}\) and not on the usual point \(x_{n}\), (6) it has eliminated the phase–lag and its derivatives up to order two, (7) it has good stability properties (i.e. interval of periodicity equal to \(\left( 0, 22 \right) \). For this method we present a detailed analysis : development, errorand stability analysis. The new proposed algorithm is applied to systems of differential equations of the Schrödinger type in order to examine its efficiency.