On efficient frequency-dependent parameters of explicit two-derivative improved Runge-Kutta-Nystro¨m method with application to two-body problem
Efficient trigonometrically-fitted explicit two-derivative improved Runge–Kutta-Nystro¨m methods with three stage fifth-order, denoted as TFTDIRKN5 method is derived for direct solving special type of second-order ordinary differential equation in the form y′(t)=f(t,y(t)) with oscillatory solution....
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-06-01
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| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016823003009 |
| _version_ | 1797839988563378176 |
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| author | K.C. Lee M.A. Alias N. Senu A. Ahmadian |
| author_facet | K.C. Lee M.A. Alias N. Senu A. Ahmadian |
| author_sort | K.C. Lee |
| collection | DOAJ |
| description | Efficient trigonometrically-fitted explicit two-derivative improved Runge–Kutta-Nystro¨m methods with three stage fifth-order, denoted as TFTDIRKN5 method is derived for direct solving special type of second-order ordinary differential equation in the form y′(t)=f(t,y(t)) with oscillatory solution. Order conditions of proposed method that includes previous estimated slopes, k-i are presented through Taylor series expansion and comparison of coefficients with power of h. Second-order initial value problems (IVPs) are integrated exactly with numerical solution in linear composition of set functions eiωt and e-iωtwith ω∈R. Certain coefficients of proposed methods are depend on the principle frequency of the numerical problems for deriving trigonometrically-fitted improved Runge–Kutta-Nystro¨m direct methods with two-derivative term. The proposed method is analysed numerically to prove that it is zero stable, consistent and convergent, which are critical for solving problems effectively. Stability region and error analysis of proposed method are investigated. The numerical tests show that the proposed method performs better in comparison with other existing Runge–Kutta-Nystro¨m methods with similar algebraic order. |
| first_indexed | 2024-04-09T16:07:02Z |
| format | Article |
| id | doaj.art-116d81334a70475eb2f11a5bb5853d7a |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-04-09T16:07:02Z |
| publishDate | 2023-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-116d81334a70475eb2f11a5bb5853d7a2023-04-25T04:07:52ZengElsevierAlexandria Engineering Journal1110-01682023-06-0172605620On efficient frequency-dependent parameters of explicit two-derivative improved Runge-Kutta-Nystro¨m method with application to two-body problemK.C. Lee0M.A. Alias1N. Senu2A. Ahmadian3Department of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia; Corresponding authors.Department of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, MalaysiaDepartment of Mathematics, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia; Corresponding authors.Decisions Lab, Mediterranea University of Reggio Calabria, Reggio Calabria, Italy; Department of Computer Science and Mathematics, Lebanese American University, Beirut, LebanonEfficient trigonometrically-fitted explicit two-derivative improved Runge–Kutta-Nystro¨m methods with three stage fifth-order, denoted as TFTDIRKN5 method is derived for direct solving special type of second-order ordinary differential equation in the form y′(t)=f(t,y(t)) with oscillatory solution. Order conditions of proposed method that includes previous estimated slopes, k-i are presented through Taylor series expansion and comparison of coefficients with power of h. Second-order initial value problems (IVPs) are integrated exactly with numerical solution in linear composition of set functions eiωt and e-iωtwith ω∈R. Certain coefficients of proposed methods are depend on the principle frequency of the numerical problems for deriving trigonometrically-fitted improved Runge–Kutta-Nystro¨m direct methods with two-derivative term. The proposed method is analysed numerically to prove that it is zero stable, consistent and convergent, which are critical for solving problems effectively. Stability region and error analysis of proposed method are investigated. The numerical tests show that the proposed method performs better in comparison with other existing Runge–Kutta-Nystro¨m methods with similar algebraic order.http://www.sciencedirect.com/science/article/pii/S1110016823003009Two-derivative improved Runge–Kutta-Nystro¨m methodsTrigonometrically-fittedSecond-order ordinary differential equationsStabilityConsistencyPeriodic problem |
| spellingShingle | K.C. Lee M.A. Alias N. Senu A. Ahmadian On efficient frequency-dependent parameters of explicit two-derivative improved Runge-Kutta-Nystro¨m method with application to two-body problem Alexandria Engineering Journal Two-derivative improved Runge–Kutta-Nystro¨m methods Trigonometrically-fitted Second-order ordinary differential equations Stability Consistency Periodic problem |
| title | On efficient frequency-dependent parameters of explicit two-derivative improved Runge-Kutta-Nystro¨m method with application to two-body problem |
| title_full | On efficient frequency-dependent parameters of explicit two-derivative improved Runge-Kutta-Nystro¨m method with application to two-body problem |
| title_fullStr | On efficient frequency-dependent parameters of explicit two-derivative improved Runge-Kutta-Nystro¨m method with application to two-body problem |
| title_full_unstemmed | On efficient frequency-dependent parameters of explicit two-derivative improved Runge-Kutta-Nystro¨m method with application to two-body problem |
| title_short | On efficient frequency-dependent parameters of explicit two-derivative improved Runge-Kutta-Nystro¨m method with application to two-body problem |
| title_sort | on efficient frequency dependent parameters of explicit two derivative improved runge kutta nystro¨m method with application to two body problem |
| topic | Two-derivative improved Runge–Kutta-Nystro¨m methods Trigonometrically-fitted Second-order ordinary differential equations Stability Consistency Periodic problem |
| url | http://www.sciencedirect.com/science/article/pii/S1110016823003009 |
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