A promising exponentially-fitted two-derivative Runge-Kutta-Nystrom method for solving y′′ = <i>f(x,y)</i>: Application to Verhulst logistic growth model

dc.authorid Senu, Norazak/0000-0001-8614-8281
dc.authorscopusid 58903782000
dc.authorscopusid 7006811882
dc.authorscopusid 55670963500
dc.authorscopusid 55602202100
dc.authorwosid Senu, Norazak/G-2776-2014
dc.contributor.author Lee, K. C.
dc.contributor.author Nazar, R.
dc.contributor.author Senu, N.
dc.contributor.author Ahmadian, A.
dc.date.accessioned 2024-05-25T11:37:25Z
dc.date.available 2024-05-25T11:37:25Z
dc.date.issued 2024
dc.department Okan University en_US
dc.department-temp [Lee, K. C.; Nazar, R.] Univ Kebangsaan Malaysia, Dept Math Sci, Bangi 43600, Selangor, Malaysia; [Senu, N.] Univ Putra Malaysia, Inst Math Res, Serdang 43400, Malaysia; [Senu, N.] Univ Putra Malaysia, Dept Math & Stat, Serdang 43400, Selangor, Malaysia; [Ahmadian, A.] Univ Mediterranea Reggio Calabria, Decis Lab, Reggio Di Calabria, Italy; [Ahmadian, A.] Lebanese Amer Univ, Dept Comp Sci & Math, Beirut, Lebanon; [Ahmadian, A.] Istanbul Okan Univ, Fac Engn & Nat Sci, Istanbul, Turkiye en_US
dc.description Senu, Norazak/0000-0001-8614-8281 en_US
dc.description.abstract Explicit exponentially-fitted two-derivative Runge-Kutta-Nystrom method with single f-function and multiple third derivatives is proposed for solving special type of second-order ordinary differential equations with exponential solutions. B-series and rooted tree theory for the proposed method are developed for the derivation of order conditions. Then, we build frequency-dependent coefficients for the proposed method by integrating the second-order initial value problem exactly with solution in the linear composition of set functions e(lambda t) and e(-lambda t) with lambda is an element of R. An exponentially-fitted two-derivative Runge-Kutta-Nystrom method with three stages fifth order is derived. Linear stability and stability region of the proposed method are analyzed. The numerical tests show that the proposed method is more effective than other existing methods with similar algebraic order in the integration of special type of second-order ordinary differential equations with exponential solutions. Also, the proposed method is used to solve a famous application problem, Verhulst logistic growth model and the result shows the proposed method still works effectively for solving this model. en_US
dc.description.sponsorship Universiti Kebangsaan Malaysia [GGPM-2023-029, ST-2022-015] en_US
dc.description.sponsorship <B>Acknowledgments</B> This study was supported by the Grant Schemes (Ref. No. GGPM-2023-029 and Ref. No. ST-2022-015) awarded by Universiti Kebangsaan Malaysia. The authors declare that there is no conflict of interest related to the publication of this paper. en_US
dc.identifier.citationcount 0
dc.identifier.doi 10.1016/j.matcom.2023.12.018
dc.identifier.endpage 49 en_US
dc.identifier.issn 0378-4754
dc.identifier.issn 1872-7166
dc.identifier.scopus 2-s2.0-85185837915
dc.identifier.scopusquality Q1
dc.identifier.startpage 28 en_US
dc.identifier.uri https://doi.org/10.1016/j.matcom.2023.12.018
dc.identifier.uri https://hdl.handle.net/20.500.14517/1157
dc.identifier.volume 219 en_US
dc.identifier.wos WOS:001141278700001
dc.identifier.wosquality Q1
dc.language.iso en
dc.publisher Elsevier en_US
dc.relation.publicationcategory Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı en_US
dc.rights info:eu-repo/semantics/openAccess en_US
dc.scopus.citedbyCount 1
dc.subject Two-derivative Runge-Kutta-Nystrom method en_US
dc.subject Second-order ordinary differential equations en_US
dc.subject Exponentially-fitted en_US
dc.subject Stability region en_US
dc.subject Numerical test en_US
dc.title A promising exponentially-fitted two-derivative Runge-Kutta-Nystrom method for solving y′′ = <i>f(x,y)</i>: Application to Verhulst logistic growth model en_US
dc.type Article en_US
dc.wos.citedbyCount 1

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