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Ali Shokri Shokri

Ali Shokri Shokri

Academic rank: Professor
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Education: PhD.
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Faculty: 1
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Research

Title
A new implicit six-step P-stable method for the numerical solution of Schrödinger equation
Type
JournalPaper
Keywords
Phase fitting; Schrödinger equation; phase-lag; ordinary differential equations; P-stable; symmetric multistep methods
Year
2020
Journal INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
DOI
Researchers Ali Shokri Shokri ، Jesús Vigo-Aguiar ، Mohammad Mehdizadeh ، Raquel Garcia-Rubio

Abstract

n this paper, we will present a new six-step P-stable method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical integration of the one-dimensional Schrödinger equation. We perform an analysis of the local truncation error of the methods for the general case and for the special case of the Schrödinger equation, where we show the decrease of the maximum power of the energy in relation to the corresponding classical methods. We also perform a periodicity analysis. In addition, we determine their periodicity regions. Finally, we compare the new methods to the corresponding classical ones and other known methods from the literature, where we show the high efficiency of the new methods.