A promising exponentially-fitted two-derivative Runge–Kutta–Nystrom method for solving y′′=f(x,y): Application to Verhulst logistic growth model
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 d...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier B.V.
2024
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| Online Access: | http://psasir.upm.edu.my/id/eprint/117789/ http://psasir.upm.edu.my/id/eprint/117789/1/117789.pdf |
| _version_ | 1848867341866106880 |
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| author | Lee, K.C. Nazar, R. Senu, N. Ahmadian, A. |
| author_facet | Lee, K.C. Nazar, R. Senu, N. Ahmadian, A. |
| author_sort | Lee, K.C. |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | 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 eλt and e−λt with λ∈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. |
| first_indexed | 2025-11-15T14:34:58Z |
| format | Article |
| id | upm-117789 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T14:34:58Z |
| publishDate | 2024 |
| publisher | Elsevier B.V. |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1177892025-06-12T03:02:37Z http://psasir.upm.edu.my/id/eprint/117789/ A promising exponentially-fitted two-derivative Runge–Kutta–Nystrom method for solving y′′=f(x,y): Application to Verhulst logistic growth model Lee, K.C. Nazar, R. Senu, N. Ahmadian, A. 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 eλt and e−λt with λ∈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. Elsevier B.V. 2024 Article PeerReviewed text en cc_by_4 http://psasir.upm.edu.my/id/eprint/117789/1/117789.pdf Lee, K.C. and Nazar, R. and Senu, N. and Ahmadian, A. (2024) A promising exponentially-fitted two-derivative Runge–Kutta–Nystrom method for solving y′′=f(x,y): Application to Verhulst logistic growth model. Mathematics and Computers in Simulation, 219. pp. 28-49. ISSN 0378-4754 https://linkinghub.elsevier.com/retrieve/pii/S0378475423005256 10.1016/j.matcom.2023.12.018 |
| spellingShingle | Lee, K.C. Nazar, R. Senu, N. Ahmadian, A. A promising exponentially-fitted two-derivative Runge–Kutta–Nystrom method for solving y′′=f(x,y): Application to Verhulst logistic growth model |
| title | A promising exponentially-fitted two-derivative Runge–Kutta–Nystrom method for solving y′′=f(x,y): Application to Verhulst logistic growth model |
| title_full | A promising exponentially-fitted two-derivative Runge–Kutta–Nystrom method for solving y′′=f(x,y): Application to Verhulst logistic growth model |
| title_fullStr | A promising exponentially-fitted two-derivative Runge–Kutta–Nystrom method for solving y′′=f(x,y): Application to Verhulst logistic growth model |
| title_full_unstemmed | A promising exponentially-fitted two-derivative Runge–Kutta–Nystrom method for solving y′′=f(x,y): Application to Verhulst logistic growth model |
| title_short | A promising exponentially-fitted two-derivative Runge–Kutta–Nystrom method for solving y′′=f(x,y): Application to Verhulst logistic growth model |
| title_sort | promising exponentially-fitted two-derivative runge–kutta–nystrom method for solving y′′=f(x,y): application to verhulst logistic growth model |
| url | http://psasir.upm.edu.my/id/eprint/117789/ http://psasir.upm.edu.my/id/eprint/117789/ http://psasir.upm.edu.my/id/eprint/117789/ http://psasir.upm.edu.my/id/eprint/117789/1/117789.pdf |