A Two-Step Modified Explicit Hybrid Method with Step-Size-Dependent Parameters for Oscillatory Problems

A Two-Step Modified Explicit Hybrid Method with Step-Size-Dependent Parameters for Oscillatory Problems

A new two-step modified explicit hybrid method with parameters depending on the step-size is constructed. This method is derived using the coefficients from a sixth-order explicit hybrid method with extended interval of absolute stability and then imposed each stage of the modified formula to exactl...

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Main Authors: Faieza Samat, Eddie Shahril Ismail
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2020/5108482
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spelling doaj-96a90952c18b4514990f14d67610cd582020-11-25T03:05:52ZengHindawi LimitedJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/51084825108482A Two-Step Modified Explicit Hybrid Method with Step-Size-Dependent Parameters for Oscillatory ProblemsFaieza Samat0Eddie Shahril Ismail1GENIUS@Pintar National Gifted Centre, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, MalaysiaDepartment of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, MalaysiaA new two-step modified explicit hybrid method with parameters depending on the step-size is constructed. This method is derived using the coefficients from a sixth-order explicit hybrid method with extended interval of absolute stability and then imposed each stage of the modified formula to exactly integrate the differential equations with solutions that can be expressed as linear combinations of sinwx and coswx, where w is the known frequency. Numerical results show the advantage of the new method for solving oscillatory problems.http://dx.doi.org/10.1155/2020/5108482
collection DOAJ
language English
format Article
sources DOAJ
author Faieza Samat
Eddie Shahril Ismail
spellingShingle Faieza Samat
Eddie Shahril Ismail
A Two-Step Modified Explicit Hybrid Method with Step-Size-Dependent Parameters for Oscillatory Problems
Journal of Mathematics
author_facet Faieza Samat
Eddie Shahril Ismail
author_sort Faieza Samat
title A Two-Step Modified Explicit Hybrid Method with Step-Size-Dependent Parameters for Oscillatory Problems
title_short A Two-Step Modified Explicit Hybrid Method with Step-Size-Dependent Parameters for Oscillatory Problems
title_full A Two-Step Modified Explicit Hybrid Method with Step-Size-Dependent Parameters for Oscillatory Problems
title_fullStr A Two-Step Modified Explicit Hybrid Method with Step-Size-Dependent Parameters for Oscillatory Problems
title_full_unstemmed A Two-Step Modified Explicit Hybrid Method with Step-Size-Dependent Parameters for Oscillatory Problems
title_sort two-step modified explicit hybrid method with step-size-dependent parameters for oscillatory problems
publisher Hindawi Limited
series Journal of Mathematics
issn 2314-4629
2314-4785
publishDate 2020-01-01
description A new two-step modified explicit hybrid method with parameters depending on the step-size is constructed. This method is derived using the coefficients from a sixth-order explicit hybrid method with extended interval of absolute stability and then imposed each stage of the modified formula to exactly integrate the differential equations with solutions that can be expressed as linear combinations of sinwx and coswx, where w is the known frequency. Numerical results show the advantage of the new method for solving oscillatory problems.
url http://dx.doi.org/10.1155/2020/5108482
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AT eddieshahrilismail atwostepmodifiedexplicithybridmethodwithstepsizedependentparametersforoscillatoryproblems
AT faiezasamat twostepmodifiedexplicithybridmethodwithstepsizedependentparametersforoscillatoryproblems
AT eddieshahrilismail twostepmodifiedexplicithybridmethodwithstepsizedependentparametersforoscillatoryproblems
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