Fourth derivative singularly P-stable method for the numerical solution of the Schrödinger equation

Abstract In this paper, we construct a method with eight steps that belongs to the family of Obrechkoff methods. Due to the explicit nature of the new method, not only does it not require another method as predictor, but it can also be considered as a suitable predictive technique to be used with im...

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Autores principales:	Ali Shokri, Higinio Ramos, Mohammad Mehdizadeh Khalsaraei, Fikret A. Aliev, Martin Bohner
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Schrödinger equation Consistency Periodicity P-stability Singularly P-stability Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/5811e44157d8483da4e8a284d18e4d43
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spelling	oai:doaj.org-article:5811e44157d8483da4e8a284d18e4d432021-11-28T12:08:23ZFourth derivative singularly P-stable method for the numerical solution of the Schrödinger equation10.1186/s13662-021-03662-91687-1847https://doaj.org/article/5811e44157d8483da4e8a284d18e4d432021-11-01T00:00:00Zhttps://doi.org/10.1186/s13662-021-03662-9https://doaj.org/toc/1687-1847Abstract In this paper, we construct a method with eight steps that belongs to the family of Obrechkoff methods. Due to the explicit nature of the new method, not only does it not require another method as predictor, but it can also be considered as a suitable predictive technique to be used with implicit methods. Periodicity and error terms are studied when applied to solve the radial Schrödinger equation, considering different energy levels. We show its advantages in terms of accuracy, consistency, and convergence in comparison with other methods of the same order appearing in the literature.Ali ShokriHiginio RamosMohammad Mehdizadeh KhalsaraeiFikret A. AlievMartin BohnerSpringerOpenarticleSchrödinger equationConsistencyPeriodicityP-stabilitySingularly P-stabilityMathematicsQA1-939ENAdvances in Difference Equations, Vol 2021, Iss 1, Pp 1-16 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Schrödinger equation Consistency Periodicity P-stability Singularly P-stability Mathematics QA1-939
spellingShingle	Schrödinger equation Consistency Periodicity P-stability Singularly P-stability Mathematics QA1-939 Ali Shokri Higinio Ramos Mohammad Mehdizadeh Khalsaraei Fikret A. Aliev Martin Bohner Fourth derivative singularly P-stable method for the numerical solution of the Schrödinger equation
description	Abstract In this paper, we construct a method with eight steps that belongs to the family of Obrechkoff methods. Due to the explicit nature of the new method, not only does it not require another method as predictor, but it can also be considered as a suitable predictive technique to be used with implicit methods. Periodicity and error terms are studied when applied to solve the radial Schrödinger equation, considering different energy levels. We show its advantages in terms of accuracy, consistency, and convergence in comparison with other methods of the same order appearing in the literature.
format	article
author	Ali Shokri Higinio Ramos Mohammad Mehdizadeh Khalsaraei Fikret A. Aliev Martin Bohner
author_facet	Ali Shokri Higinio Ramos Mohammad Mehdizadeh Khalsaraei Fikret A. Aliev Martin Bohner
author_sort	Ali Shokri
title	Fourth derivative singularly P-stable method for the numerical solution of the Schrödinger equation
title_short	Fourth derivative singularly P-stable method for the numerical solution of the Schrödinger equation
title_full	Fourth derivative singularly P-stable method for the numerical solution of the Schrödinger equation
title_fullStr	Fourth derivative singularly P-stable method for the numerical solution of the Schrödinger equation
title_full_unstemmed	Fourth derivative singularly P-stable method for the numerical solution of the Schrödinger equation
title_sort	fourth derivative singularly p-stable method for the numerical solution of the schrödinger equation
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/5811e44157d8483da4e8a284d18e4d43
work_keys_str_mv	AT alishokri fourthderivativesingularlypstablemethodforthenumericalsolutionoftheschrodingerequation AT higinioramos fourthderivativesingularlypstablemethodforthenumericalsolutionoftheschrodingerequation AT mohammadmehdizadehkhalsaraei fourthderivativesingularlypstablemethodforthenumericalsolutionoftheschrodingerequation AT fikretaaliev fourthderivativesingularlypstablemethodforthenumericalsolutionoftheschrodingerequation AT martinbohner fourthderivativesingularlypstablemethodforthenumericalsolutionoftheschrodingerequation
_version_	1718408198296174592

Fourth derivative singularly P-stable method for the numerical solution of the Schrödinger equation

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