A new fourteenth algebraic order finite difference method for the approximate solution of the Schrödinger equation

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• 作者：Jianbin Zhao ; T. E. Simos
• 关键词：Phase ; lag ; Derivative of the phase ; lag ; Initial value problems ; Oscillating solution ; Symmetric ; Hybrid ; Multistep ; Hybrid ; 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：697-716
• 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 the present paper we will develop and analyse a new five-stages symmetric two-step method of high algebraic order with vanished phase-lag and its first, second, third, fourth and fifth derivatives. We will construct the new method. We will compute its local local truncation error (LTE). We will produce the asymptotic form of the LTE applying the new method to the radial time independent Schrödinger equation and we will compare it with other asymptotic forms of LTE of similar methods. Applying the new method to a scalar test equation with frequency different than the frequency of the scalar test equation used for the phase-lag analysis, we will investigate the stability and the interval of periodicity of the new method based and we will compare the produced interval of periodicity with other intervals of similar methods. Finally, we will examine the effectiveness of the new method applying it to the coupled Schrödinger equations.