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Lim, Jin Yoong, Lee, Khai Chien, Aziz, Nurul Huda, Sun, Zhuoyu, Senu, Norazak. (1405). Enhanced multistep two-derivative Runge-Kutta methods: application to coupled spring systems. سامانه مدیریت نشریات علمی, (), -. doi: 10.22034/cmde.2026.67441.3211
Jin Yoong Lim; Khai Chien Lee; Nurul Huda Abdul Aziz; Zhuoyu Sun; Norazak Senu. "Enhanced multistep two-derivative Runge-Kutta methods: application to coupled spring systems". سامانه مدیریت نشریات علمی, , , 1405, -. doi: 10.22034/cmde.2026.67441.3211
Lim, Jin Yoong, Lee, Khai Chien, Aziz, Nurul Huda, Sun, Zhuoyu, Senu, Norazak. (1405). 'Enhanced multistep two-derivative Runge-Kutta methods: application to coupled spring systems', سامانه مدیریت نشریات علمی, (), pp. -. doi: 10.22034/cmde.2026.67441.3211
Lim, Jin Yoong, Lee, Khai Chien, Aziz, Nurul Huda, Sun, Zhuoyu, Senu, Norazak. Enhanced multistep two-derivative Runge-Kutta methods: application to coupled spring systems. سامانه مدیریت نشریات علمی, 1405; (): -. doi: 10.22034/cmde.2026.67441.3211

Enhanced multistep two-derivative Runge-Kutta methods: application to coupled spring systems

Computational Methods for Differential Equations
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 17 شهریور 1405    اصل مقاله (1.47 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2026.67441.3211
نویسندگان
Jin Yoong Lim1؛ Khai Chien Lee* 2؛ Nurul Huda Abdul Aziz* 3؛ Zhuoyu Sun1؛ Norazak Senu4
1Institute of Actuarial Science and Data Analytics, UCSI University, 56000 Cheras, Kuala Lumpur, Malaysia.
2Department of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia.
3Institute of Engineering Mathematics, University of Malaysia Perli, 02600 Arau, Perlis, Malaysia.
41. Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia. 2. Department of Mathematics and Statistics, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia.
چکیده
Explicit multistep two-derivative Runge–Kutta methods with single $f$--evaluation and
multiple $g$--evaluations whilst incorporating the value of 2 step-points $x_i$ and
$x_{i-1}$ is proposed for solving first-order ordinary differential equations with
exponential solutions. The proposed methods are constructed based on the algebraic order
conditions derived from Taylor series expansion. Then, multistep two-derivative
Runge–Kutta (MTDRK) methods of two-stages fourth order and three-stages fifth order,
are derived. The properties of linear stability, stability region and convergence for both
MTDRK methods are analyzed. The numerical tests show that the proposed method is more
effective than other existing methods with similar algebraic order in solving first-order
ordinary differential equations. Also, the proposed method is used to solve a coupled
springs system, and the results show that the proposed methods work effectively for
solving this model.
کلیدواژه‌ها
two-derivative Runge-Kutta methods؛ multistep؛ first-order ODEs؛ stability؛ coupled spring systems
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تعداد مشاهده مقاله: 2


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