دوره 13، شماره 1 - ( 2-1397 )                   جلد 13 شماره 1 صفحات 111-129 | برگشت به فهرست نسخه ها

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Shokri A, Saadat H, Khodadadi A R. A New High Order Closed Newton-Cotes Trigonometrically-fitted Formulae for the Numerical Solution of the Schrodinger Equation. IJMSI. 2018; 13 (1) :111-129
URL: http://ijmsi.ir/article-1-785-fa.html
A New High Order Closed Newton-Cotes Trigonometrically-fitted Formulae for the Numerical Solution of the Schrodinger Equation. مجله علوم ریاضی و انفورماتیک ایرانیان. 1397; 13 (1) :111-129

URL: http://ijmsi.ir/article-1-785-fa.html


چکیده:  

In this paper, we investigate the connection between closed Newton-Cotes formulae, trigonometrically-fitted methods, symplectic integrators and efficient integration of the Schr¨odinger equation. The study of multistep symplectic integrators is very poor although in the last decades several one step symplectic integrators have been produced based on symplectic geometry (see the relevant literature and the references here). In this paper we study the closed Newton-Cotes formulae and we write them as symplectic multilayer structures. Based on the closed Newton-Cotes formulae, we also develop trigonometrically-fitted symplectic methods. An error analysis for the onedimensional Schrodinger equation of the new developed methods and a comparison with previous developed methods is also given. We apply the new symplectic schemes to the well-known radial Schr¨odinger equation in order to investigate the efficiency of the proposed method to these type of problems.

نوع مطالعه: پژوهشي | موضوع مقاله: تخصصي

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