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فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

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Hippolyte, Sèka, Konan Firmin, N'gohissè, Manin Mathurin, Taha. (1405). RESIDUAL-BASED OPTIMIZATION OF FIFTH-ORDER RUNGE-KUTTA METHODS. سامانه مدیریت نشریات علمی, (), -. doi: 10.22034/cmde.2026.72086.3632
Sèka Hippolyte; N'gohissè Konan Firmin; Taha Manin Mathurin. "RESIDUAL-BASED OPTIMIZATION OF FIFTH-ORDER RUNGE-KUTTA METHODS". سامانه مدیریت نشریات علمی, , , 1405, -. doi: 10.22034/cmde.2026.72086.3632
Hippolyte, Sèka, Konan Firmin, N'gohissè, Manin Mathurin, Taha. (1405). 'RESIDUAL-BASED OPTIMIZATION OF FIFTH-ORDER RUNGE-KUTTA METHODS', سامانه مدیریت نشریات علمی, (), pp. -. doi: 10.22034/cmde.2026.72086.3632
Hippolyte, Sèka, Konan Firmin, N'gohissè, Manin Mathurin, Taha. RESIDUAL-BASED OPTIMIZATION OF FIFTH-ORDER RUNGE-KUTTA METHODS. سامانه مدیریت نشریات علمی, 1405; (): -. doi: 10.22034/cmde.2026.72086.3632

RESIDUAL-BASED OPTIMIZATION OF FIFTH-ORDER RUNGE-KUTTA METHODS

Computational Methods for Differential Equations
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 29 مهر 1405    اصل مقاله (1.43 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2026.72086.3632
نویسندگان
Sèka Hippolyte* 1؛ N'gohissè Konan Firmin2؛ Taha Manin Mathurin1
1Institut National Polytechnique Félix Houphouët-Boigny, Côte d’Ivoire.
2Université Péléforo GON COULIBALY, Côte d’Ivoire.
چکیده
In this work, we study a parametric family of fifth-order Runge--Kutta methods depending on a free parameter and their optimization using an approach based on minimizing the sum of squares of the residuals associated with higher-order conditions. Unlike the classical approach restricted to conditions of order 6, we successively consider conditions of orders 6, 7, and 8 in order to assess their influence on the quality of the optimization. The results suggest that the use of order-8 conditions in the construction of the error function may lead, in several cases, to improved satisfaction of higher-order conditions compared with optimizations based on orders 6 or 7. This improvement appears to result from a more comprehensive reduction of higher-order approximation defects, allowing a more balanced distribution of errors. This study highlights the interest of incorporating higher-order conditions into optimization procedures for Runge--Kutta methods and provides a residual-based strategy for selecting free parameters in parametric families of methods. Finally, the optimized methods obtained are compared with the classical Butcher, Fehlberg, and Dormand--Prince methods.
کلیدواژه‌ها
Runge--Kutta methods؛ order conditions؛ residual minimization؛ numerical methods for ODEs؛ Butcher theory
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تعداد مشاهده مقاله: 1


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