Iranian Journal of Mathematical Sciences and Informatics
مجله علوم ریاضی و انفورماتیک ایرانیان
IJMSI
Basic Sciences
http://ijmsi.ir
1
admin
1735-4463
2008-9473
8
7
14
8888
13
en
jalali
1397
2
1
gregorian
2018
5
1
13
1
online
1
fulltext
en
A New High Order Closed Newton-Cotes Trigonometrically-fitted Formulae for the Numerical Solution of the Schrodinger Equation
تخصصي
Special
پژوهشي
Research paper
<p>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.</p>
Phase-lag, Schrodinger equation, Numerical solution, Newton-Cotes formulae, Derivative
111
129
http://ijmsi.ir/browse.php?a_code=A-10-1649-1&slc_lang=en&sid=1
A.
Shokri
shokri@maragheh.ac.ir
`10031947532846004626`

10031947532846004626
Yes
Faculty of Mathematical Science, University of Maragheh, Maragheh, Iran
H.
Saadat
hosein67saadat@yahoo.com
`10031947532846004627`

10031947532846004627
No
Faculty of Mathematical Science, University of Maragheh, Maragheh, Iran
A. R.
Khodadadi
ali_reza_khodadadi@yahoo.com
`10031947532846004628`

10031947532846004628
No
Faculty of Mathematical Science, University of Maragheh, Maragheh, Iran