Numerical solution of delay differential equation using two-derivative Runge-Kutta type method with Newton interpolation
Numerical approach of two-derivative Runge-Kutta type method with three-stage fifth-order (TDRKT3(5)) is developed and proposed for solving a special type of third-order delay differential equations (DDEs) with constant delay. An algorithm based on Newton interpolation and hybrid with the TDRKT meth...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2022-08-01
|
| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016821007353 |
| _version_ | 1818521030635814912 |
|---|---|
| author | N. Senu K.C. Lee A. Ahmadian S.N.I. Ibrahim |
| author_facet | N. Senu K.C. Lee A. Ahmadian S.N.I. Ibrahim |
| author_sort | N. Senu |
| collection | DOAJ |
| description | Numerical approach of two-derivative Runge-Kutta type method with three-stage fifth-order (TDRKT3(5)) is developed and proposed for solving a special type of third-order delay differential equations (DDEs) with constant delay. An algorithm based on Newton interpolation and hybrid with the TDRKT method is built to approximate the solution of third-order DDEs. In this paper, three-stage fifth-order called TDRKT3(5) method with single third derivative and multiple evaluations of the fourth derivative is highlighted to solve third-order pantograph type delay differential equations directly with the aid of the Newton interpolation method. Stability analysis of TDRKT3(5) method is investigated. The numerical experiments illustrate high efficiency and validity of the new method for solving a special class of third-order DDEs and some future works are recommended by extending proposed method to solve fractional and singularly perturbed delay differential equations. |
| first_indexed | 2024-12-11T01:45:33Z |
| format | Article |
| id | doaj.art-f37fad6c65744bbc9856ac9bf5fa835a |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-12-11T01:45:33Z |
| publishDate | 2022-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-f37fad6c65744bbc9856ac9bf5fa835a2022-12-22T01:24:55ZengElsevierAlexandria Engineering Journal1110-01682022-08-0161858195835Numerical solution of delay differential equation using two-derivative Runge-Kutta type method with Newton interpolationN. Senu0K.C. Lee1A. Ahmadian2S.N.I. Ibrahim3Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia; Department of Mathematics and Statistics, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia; Corresponding author at: Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia.Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, MalaysiaInstitute of Industry Revolution 4.0, The National University of Malaysia, 43600 UKM Bangi, Selangor, MalaysiaInstitute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia; Department of Mathematics and Statistics, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, MalaysiaNumerical approach of two-derivative Runge-Kutta type method with three-stage fifth-order (TDRKT3(5)) is developed and proposed for solving a special type of third-order delay differential equations (DDEs) with constant delay. An algorithm based on Newton interpolation and hybrid with the TDRKT method is built to approximate the solution of third-order DDEs. In this paper, three-stage fifth-order called TDRKT3(5) method with single third derivative and multiple evaluations of the fourth derivative is highlighted to solve third-order pantograph type delay differential equations directly with the aid of the Newton interpolation method. Stability analysis of TDRKT3(5) method is investigated. The numerical experiments illustrate high efficiency and validity of the new method for solving a special class of third-order DDEs and some future works are recommended by extending proposed method to solve fractional and singularly perturbed delay differential equations.http://www.sciencedirect.com/science/article/pii/S1110016821007353Runge-Kutta type methodsThird-order delay differential equationsPantograph type delay differential equationsNewton interpolation methodStability |
| spellingShingle | N. Senu K.C. Lee A. Ahmadian S.N.I. Ibrahim Numerical solution of delay differential equation using two-derivative Runge-Kutta type method with Newton interpolation Alexandria Engineering Journal Runge-Kutta type methods Third-order delay differential equations Pantograph type delay differential equations Newton interpolation method Stability |
| title | Numerical solution of delay differential equation using two-derivative Runge-Kutta type method with Newton interpolation |
| title_full | Numerical solution of delay differential equation using two-derivative Runge-Kutta type method with Newton interpolation |
| title_fullStr | Numerical solution of delay differential equation using two-derivative Runge-Kutta type method with Newton interpolation |
| title_full_unstemmed | Numerical solution of delay differential equation using two-derivative Runge-Kutta type method with Newton interpolation |
| title_short | Numerical solution of delay differential equation using two-derivative Runge-Kutta type method with Newton interpolation |
| title_sort | numerical solution of delay differential equation using two derivative runge kutta type method with newton interpolation |
| topic | Runge-Kutta type methods Third-order delay differential equations Pantograph type delay differential equations Newton interpolation method Stability |
| url | http://www.sciencedirect.com/science/article/pii/S1110016821007353 |
| work_keys_str_mv | AT nsenu numericalsolutionofdelaydifferentialequationusingtwoderivativerungekuttatypemethodwithnewtoninterpolation AT kclee numericalsolutionofdelaydifferentialequationusingtwoderivativerungekuttatypemethodwithnewtoninterpolation AT aahmadian numericalsolutionofdelaydifferentialequationusingtwoderivativerungekuttatypemethodwithnewtoninterpolation AT sniibrahim numericalsolutionofdelaydifferentialequationusingtwoderivativerungekuttatypemethodwithnewtoninterpolation |