jzs-10817

A Numerical Algorithm for the Schrödinger Type Differential Equation with Time Involution

 Allaberen Ashyralyev1,2,3, and  Twana Hidayat1

1 Department of Mathematics, Near East University, Nicosia, Mersin 10, Turkey.

2 Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St,Moscow 117198, Russian Federation.

3 Institute of Mathematics and Mathematical Modeling, 050010, Almaty,Kazakhstan.

*Corresponding author’s e-mail: twana.margaret@gmail.com

Original: 7 August 2020        Revised: 5 September 2020        Accepted: 26 September 2020        Published online: 20 December 2020

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Abstract

The initial boundary value problem for the one dimensional (SE) with time involution and Neumann condition is investigated. The theorem on stability this problem is proved. New absolute stable difference schemes (DSs) for this involution problem are constucted. The theorem on stability the first order of accuracy difference scheme is established. The algorithm has been built for these (DSs), a program is written, examples are presented, and numerical results have been tabulated. Comparisons of errors are made between the exact and numerical solutions in maximum norm. All the computer programs are written in Matlab. 

Key Words: Schrödinger equation, Involution, Stability, Difference scheme

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