Sixth Order Numerov-Type Methods with Coefficients Trained to Perform Best on Problems with Oscillating Solutions

Numerov-type methods using four stages per step and sharing sixth algebraic order are considered. The coefficients of such methods are depended on two free parameters. For addressing problems with oscillatory solutions, we traditionally try to satisfy some specific properties such as reduce the phas...

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Autores principales:	Vladislav N. Kovalnogov, Ruslan V. Fedorov, Tamara V. Karpukhina, Theodore E. Simos, Charalampos Tsitouras
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	initial value problem numerov methods differential evolution periodic solutions Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/8daf2e4af1c0420bab3b9fead9617313
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spelling	oai:doaj.org-article:8daf2e4af1c0420bab3b9fead96173132021-11-11T18:18:07ZSixth Order Numerov-Type Methods with Coefficients Trained to Perform Best on Problems with Oscillating Solutions10.3390/math92127562227-7390https://doaj.org/article/8daf2e4af1c0420bab3b9fead96173132021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2756https://doaj.org/toc/2227-7390Numerov-type methods using four stages per step and sharing sixth algebraic order are considered. The coefficients of such methods are depended on two free parameters. For addressing problems with oscillatory solutions, we traditionally try to satisfy some specific properties such as reduce the phase-lag error, extend the interval of periodicity or even nullify the amplification. All of these latter properties come from a test problem that poses as a solution to an ideal trigonometric orbit. Here, we propose the training of the coefficients of the selected family of methods in a wide set of relevant problems. After performing this training using the differential evolution technique, we arrive at a certain method that outperforms the other ones from this family in an even wider set of oscillatory problems.Vladislav N. KovalnogovRuslan V. FedorovTamara V. KarpukhinaTheodore E. SimosCharalampos TsitourasMDPI AGarticleinitial value problemnumerov methodsdifferential evolutionperiodic solutionsMathematicsQA1-939ENMathematics, Vol 9, Iss 2756, p 2756 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	initial value problem numerov methods differential evolution periodic solutions Mathematics QA1-939
spellingShingle	initial value problem numerov methods differential evolution periodic solutions Mathematics QA1-939 Vladislav N. Kovalnogov Ruslan V. Fedorov Tamara V. Karpukhina Theodore E. Simos Charalampos Tsitouras Sixth Order Numerov-Type Methods with Coefficients Trained to Perform Best on Problems with Oscillating Solutions
description	Numerov-type methods using four stages per step and sharing sixth algebraic order are considered. The coefficients of such methods are depended on two free parameters. For addressing problems with oscillatory solutions, we traditionally try to satisfy some specific properties such as reduce the phase-lag error, extend the interval of periodicity or even nullify the amplification. All of these latter properties come from a test problem that poses as a solution to an ideal trigonometric orbit. Here, we propose the training of the coefficients of the selected family of methods in a wide set of relevant problems. After performing this training using the differential evolution technique, we arrive at a certain method that outperforms the other ones from this family in an even wider set of oscillatory problems.
format	article
author	Vladislav N. Kovalnogov Ruslan V. Fedorov Tamara V. Karpukhina Theodore E. Simos Charalampos Tsitouras
author_facet	Vladislav N. Kovalnogov Ruslan V. Fedorov Tamara V. Karpukhina Theodore E. Simos Charalampos Tsitouras
author_sort	Vladislav N. Kovalnogov
title	Sixth Order Numerov-Type Methods with Coefficients Trained to Perform Best on Problems with Oscillating Solutions
title_short	Sixth Order Numerov-Type Methods with Coefficients Trained to Perform Best on Problems with Oscillating Solutions
title_full	Sixth Order Numerov-Type Methods with Coefficients Trained to Perform Best on Problems with Oscillating Solutions
title_fullStr	Sixth Order Numerov-Type Methods with Coefficients Trained to Perform Best on Problems with Oscillating Solutions
title_full_unstemmed	Sixth Order Numerov-Type Methods with Coefficients Trained to Perform Best on Problems with Oscillating Solutions
title_sort	sixth order numerov-type methods with coefficients trained to perform best on problems with oscillating solutions
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/8daf2e4af1c0420bab3b9fead9617313
work_keys_str_mv	AT vladislavnkovalnogov sixthordernumerovtypemethodswithcoefficientstrainedtoperformbestonproblemswithoscillatingsolutions AT ruslanvfedorov sixthordernumerovtypemethodswithcoefficientstrainedtoperformbestonproblemswithoscillatingsolutions AT tamaravkarpukhina sixthordernumerovtypemethodswithcoefficientstrainedtoperformbestonproblemswithoscillatingsolutions AT theodoreesimos sixthordernumerovtypemethodswithcoefficientstrainedtoperformbestonproblemswithoscillatingsolutions AT charalampostsitouras sixthordernumerovtypemethodswithcoefficientstrainedtoperformbestonproblemswithoscillatingsolutions
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Sixth Order Numerov-Type Methods with Coefficients Trained to Perform Best on Problems with Oscillating Solutions

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