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Ali Shokri Shokri

Ali Shokri Shokri

Academic rank: Professor
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Education: PhD.
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Research

Title
The New Classes of High Order Implicit Six-Step P-Stable Multiderivative Methods 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 Applied and Computational Mathematics
DOI
Researchers Mohammad Mehdizadeh ، Ali Shokri Shokri

Abstract

In this paper, we present the new class of six-step P-stable multiderivative methods of eighth (and tenth) algebraic order with vanishing phase-lag and its first, second, third, fourth (and fifth) derivatives for the numerical integration of the one-dimensional Schrodinger equation. We perform an analysis of the local truncation error of the methods for the general and special cases of the Schrödinger equation, where we show the decrease of the maximum power of the energy in relation to the corresponding classical methods. For the produced methods we investigate their errors and stability. Based on the above mentioned analysis we give some remarks and conclusions about their efficacy in the numerical integration of the radial Schrödinger equation.