Efficient frequency-dependent coefficients of explicit improved two-derivative Runge-Kutta type methods for solving third order IVPs
This study aims to propose sixth-order two-derivative improved Runge-Kutta type methods adopted with exponentially-fitting and trigonometrically-fitting techniques for integrating a special type of third-order ordinary differential equation in the form u'''(t)=f(t,u(t),u'(t)). Th...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Universiti Putra Malaysia Press
2023
|
| Online Access: | http://psasir.upm.edu.my/id/eprint/107629/1/10%20JST-3669-2022.pdf |
| _version_ | 1811137803304566784 |
|---|---|
| author | Chien, Lee Khai Senu, Norazak Ahmadian, Ali Ibrahim, Siti Nur Iqmal |
| author_facet | Chien, Lee Khai Senu, Norazak Ahmadian, Ali Ibrahim, Siti Nur Iqmal |
| author_sort | Chien, Lee Khai |
| collection | UPM |
| description | This study aims to propose sixth-order two-derivative improved Runge-Kutta type methods adopted with exponentially-fitting and trigonometrically-fitting techniques for integrating a special type of third-order ordinary differential equation in the form u'''(t)=f(t,u(t),u'(t)). The procedure of constructing order conditions comprised of a few previous steps, k-i for third-order two-derivative Runge-Kutta-type methods, has been outlined. These methods are developed through the idea of integrating initial value problems exactly with a numerical solution in the form of linear composition of the set functions eѡt and e-ѡtfor exponentially fitted and eiѡt and e-iѡt for trigonometrically-fitted with ѡ ϵ R. Parameters of two-derivative Runge-Kutta type method are adapted into principle frequency of exponential and oscillatory problems to construct the proposed methods. Error analysis of proposed methods is analysed, and the computational efficiency of proposed methods is demonstrated in numerical experiments compared to other existing numerical methods for integrating third-order ordinary differential equations with an exponential and periodic solution. |
| first_indexed | 2024-09-25T03:40:06Z |
| format | Article |
| id | upm.eprints-107629 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-09-25T03:40:06Z |
| publishDate | 2023 |
| publisher | Universiti Putra Malaysia Press |
| record_format | dspace |
| spelling | upm.eprints-1076292024-09-09T03:50:28Z http://psasir.upm.edu.my/id/eprint/107629/ Efficient frequency-dependent coefficients of explicit improved two-derivative Runge-Kutta type methods for solving third order IVPs Chien, Lee Khai Senu, Norazak Ahmadian, Ali Ibrahim, Siti Nur Iqmal This study aims to propose sixth-order two-derivative improved Runge-Kutta type methods adopted with exponentially-fitting and trigonometrically-fitting techniques for integrating a special type of third-order ordinary differential equation in the form u'''(t)=f(t,u(t),u'(t)). The procedure of constructing order conditions comprised of a few previous steps, k-i for third-order two-derivative Runge-Kutta-type methods, has been outlined. These methods are developed through the idea of integrating initial value problems exactly with a numerical solution in the form of linear composition of the set functions eѡt and e-ѡtfor exponentially fitted and eiѡt and e-iѡt for trigonometrically-fitted with ѡ ϵ R. Parameters of two-derivative Runge-Kutta type method are adapted into principle frequency of exponential and oscillatory problems to construct the proposed methods. Error analysis of proposed methods is analysed, and the computational efficiency of proposed methods is demonstrated in numerical experiments compared to other existing numerical methods for integrating third-order ordinary differential equations with an exponential and periodic solution. Universiti Putra Malaysia Press 2023-03-20 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/107629/1/10%20JST-3669-2022.pdf Chien, Lee Khai and Senu, Norazak and Ahmadian, Ali and Ibrahim, Siti Nur Iqmal (2023) Efficient frequency-dependent coefficients of explicit improved two-derivative Runge-Kutta type methods for solving third order IVPs. Pertanika Journal of Science and Technology, 31 (2). pp. 843-873. ISSN 0128-7680; ESSN: 2231-8526 http://www.pertanika.upm.edu.my/pjst/browse/regular-issue?article=JST-3669-2022 10.47836/pjst.31.2.10 |
| spellingShingle | Chien, Lee Khai Senu, Norazak Ahmadian, Ali Ibrahim, Siti Nur Iqmal Efficient frequency-dependent coefficients of explicit improved two-derivative Runge-Kutta type methods for solving third order IVPs |
| title | Efficient frequency-dependent coefficients of explicit improved two-derivative Runge-Kutta type methods for solving third order IVPs |
| title_full | Efficient frequency-dependent coefficients of explicit improved two-derivative Runge-Kutta type methods for solving third order IVPs |
| title_fullStr | Efficient frequency-dependent coefficients of explicit improved two-derivative Runge-Kutta type methods for solving third order IVPs |
| title_full_unstemmed | Efficient frequency-dependent coefficients of explicit improved two-derivative Runge-Kutta type methods for solving third order IVPs |
| title_short | Efficient frequency-dependent coefficients of explicit improved two-derivative Runge-Kutta type methods for solving third order IVPs |
| title_sort | efficient frequency dependent coefficients of explicit improved two derivative runge kutta type methods for solving third order ivps |
| url | http://psasir.upm.edu.my/id/eprint/107629/1/10%20JST-3669-2022.pdf |
| work_keys_str_mv | AT chienleekhai efficientfrequencydependentcoefficientsofexplicitimprovedtwoderivativerungekuttatypemethodsforsolvingthirdorderivps AT senunorazak efficientfrequencydependentcoefficientsofexplicitimprovedtwoderivativerungekuttatypemethodsforsolvingthirdorderivps AT ahmadianali efficientfrequencydependentcoefficientsofexplicitimprovedtwoderivativerungekuttatypemethodsforsolvingthirdorderivps AT ibrahimsitinuriqmal efficientfrequencydependentcoefficientsofexplicitimprovedtwoderivativerungekuttatypemethodsforsolvingthirdorderivps |