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Jasim, Athraa, SENU, NORAZAK, Abdul Majid, Zanariah, NIK LONG, Nik Mohd Asri. (1403). Higher-order multi-step Runge-Kutta-Nystrom methods with frequency dependent coefficients for second-order initial value problem u''=f(x,u,u'). سامانه مدیریت نشریات علمی, (), -. doi: 10.22034/cmde.2024.57684.2418
Athraa Abdulsalam Jasim; NORAZAK SENU; Zanariah Abdul Majid; Nik Mohd Asri NIK LONG. "Higher-order multi-step Runge-Kutta-Nystrom methods with frequency dependent coefficients for second-order initial value problem u''=f(x,u,u')". سامانه مدیریت نشریات علمی, , , 1403, -. doi: 10.22034/cmde.2024.57684.2418
Jasim, Athraa, SENU, NORAZAK, Abdul Majid, Zanariah, NIK LONG, Nik Mohd Asri. (1403). 'Higher-order multi-step Runge-Kutta-Nystrom methods with frequency dependent coefficients for second-order initial value problem u''=f(x,u,u')', سامانه مدیریت نشریات علمی, (), pp. -. doi: 10.22034/cmde.2024.57684.2418
Jasim, Athraa, SENU, NORAZAK, Abdul Majid, Zanariah, NIK LONG, Nik Mohd Asri. Higher-order multi-step Runge-Kutta-Nystrom methods with frequency dependent coefficients for second-order initial value problem u''=f(x,u,u'). سامانه مدیریت نشریات علمی, 1403; (): -. doi: 10.22034/cmde.2024.57684.2418

Higher-order multi-step Runge-Kutta-Nystrom methods with frequency dependent coefficients for second-order initial value problem u''=f(x,u,u')

Computational Methods for Differential Equations
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 28 فروردین 1403    اصل مقاله (1.34 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.57684.2418
نویسندگان
Athraa Abdulsalam Jasim1؛ NORAZAK SENU* 2؛ Zanariah Abdul Majid3؛ Nik Mohd Asri NIK LONG2
11- Institute for Mathematical Research, Universiti Putra Malaysia, UPM, Serdang 43400, Selangor, Malaysia. 2- Department of Mathematics and Computer Applications, College of Sciences, Al-Nahrain University, Jadriya, Baghdad, Iraq.
21- Department of Mathematics and Statistics, Universiti Putra Malaysia, UPM, Serdang 43400, Selangor, Malaysia. 2- Institute for Mathematical Research, Universiti Putra Malaysia, UPM, Serdang 43400, Selangor, Malaysia.
31- Institute for Mathematical Research, Universiti Putra Malaysia, UPM, Serdang 43400, Selangor, Malaysia. 2- Department of Mathematics and Statistics, Universiti Putra Malaysia, UPM, Serdang 43400, Selangor, Malaysia.
چکیده
In this study, for the numerical solution of general second-order ordinary differential equations (ODEs) that exhibit oscillatory or periodic behavior, fifth- and sixth-order explicit multi-step Runge-Kutta-Nystrom (MSGRKN) methods, respectively, are constructed. The parameters of the proposed methods rely on the frequency $\omega$ of each problem whose solution is a linear combination of functions $\{e^{ (i \omega x)},\quad e^{ (-i \omega x)}\}$ or $\{\cos (\omega x),\quad \sin (\omega x)\}$. The study also includes an analysis of the linear stability of the suggested methods. The numerical results indicate the efficiency of the proposed methods in solving such problems compared to methods with similar characteristics in the literature.
کلیدواژه‌ها
Explicit methods؛ trigonometrical fitting؛ multi-step Runge-Kutta-Nystrom methods؛ initial value problems؛ general second-order oscillatory differential equations
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تعداد مشاهده مقاله: 53
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