Solution for nonlinear Duffing oscillator using variable order variable stepsize block method
Real life phenomena found in various fields such as engineering, physics, biology and communication theory can be modeled as nonlinear higher order ordinary differential equations, particularly the Duffing oscillator. Analytical solutions for these differential equations can be time consuming wherea...
| Main Authors: | , , , , , , , |
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| Format: | Article |
| Language: | English |
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Penerbit UTM Press
2017
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| Online Access: | http://psasir.upm.edu.my/id/eprint/64097/1/Solution%20for%20nonlinear%20Duffing%20oscillator%20using%20variable%20order%20variable%20stepsize%20block%20method.pdf |
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| author | Rasedee, Ahmad Fadly Nurullah Abdul Sathar, Mohamad Hasan Ishak, Norizarina Kamarudin, Nur Shuhada Nazri, Muhamad Azrin Ramli, Nur Ainna Ismail, Irneza Sahrim, Mus'ab |
| author_facet | Rasedee, Ahmad Fadly Nurullah Abdul Sathar, Mohamad Hasan Ishak, Norizarina Kamarudin, Nur Shuhada Nazri, Muhamad Azrin Ramli, Nur Ainna Ismail, Irneza Sahrim, Mus'ab |
| author_sort | Rasedee, Ahmad Fadly Nurullah |
| collection | UPM |
| description | Real life phenomena found in various fields such as engineering, physics, biology and communication theory can be modeled as nonlinear higher order ordinary differential equations, particularly the Duffing oscillator. Analytical solutions for these differential equations can be time consuming whereas, conventional numerical solutions may lack accuracy. This research propose a block multistep method integrated with a variable order step size (VOS) algorithm for solving these Duffing oscillators directly. The proposed VOS Block method provides an alternative numerical solution by reducing computational cost (time) but without loss of accuracy. Numerical simulations are compared with known exact solutions for proof of accuracy and against current numerical methods for proof of efficiency (steps taken). |
| first_indexed | 2024-03-06T09:45:49Z |
| format | Article |
| id | upm.eprints-64097 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:45:49Z |
| publishDate | 2017 |
| publisher | Penerbit UTM Press |
| record_format | dspace |
| spelling | upm.eprints-640972018-06-11T08:17:56Z http://psasir.upm.edu.my/id/eprint/64097/ Solution for nonlinear Duffing oscillator using variable order variable stepsize block method Rasedee, Ahmad Fadly Nurullah Abdul Sathar, Mohamad Hasan Ishak, Norizarina Kamarudin, Nur Shuhada Nazri, Muhamad Azrin Ramli, Nur Ainna Ismail, Irneza Sahrim, Mus'ab Real life phenomena found in various fields such as engineering, physics, biology and communication theory can be modeled as nonlinear higher order ordinary differential equations, particularly the Duffing oscillator. Analytical solutions for these differential equations can be time consuming whereas, conventional numerical solutions may lack accuracy. This research propose a block multistep method integrated with a variable order step size (VOS) algorithm for solving these Duffing oscillators directly. The proposed VOS Block method provides an alternative numerical solution by reducing computational cost (time) but without loss of accuracy. Numerical simulations are compared with known exact solutions for proof of accuracy and against current numerical methods for proof of efficiency (steps taken). Penerbit UTM Press 2017 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/64097/1/Solution%20for%20nonlinear%20Duffing%20oscillator%20using%20variable%20order%20variable%20stepsize%20block%20method.pdf Rasedee, Ahmad Fadly Nurullah and Abdul Sathar, Mohamad Hasan and Ishak, Norizarina and Kamarudin, Nur Shuhada and Nazri, Muhamad Azrin and Ramli, Nur Ainna and Ismail, Irneza and Sahrim, Mus'ab (2017) Solution for nonlinear Duffing oscillator using variable order variable stepsize block method. Matematika, 33 (2). pp. 165-175. ISSN 0127-8274 https://matematika.utm.my/index.php/matematika/article/view/1015 10.11113/matematika.v33.n2.1015 |
| spellingShingle | Rasedee, Ahmad Fadly Nurullah Abdul Sathar, Mohamad Hasan Ishak, Norizarina Kamarudin, Nur Shuhada Nazri, Muhamad Azrin Ramli, Nur Ainna Ismail, Irneza Sahrim, Mus'ab Solution for nonlinear Duffing oscillator using variable order variable stepsize block method |
| title | Solution for nonlinear Duffing oscillator using variable order variable stepsize block method |
| title_full | Solution for nonlinear Duffing oscillator using variable order variable stepsize block method |
| title_fullStr | Solution for nonlinear Duffing oscillator using variable order variable stepsize block method |
| title_full_unstemmed | Solution for nonlinear Duffing oscillator using variable order variable stepsize block method |
| title_short | Solution for nonlinear Duffing oscillator using variable order variable stepsize block method |
| title_sort | solution for nonlinear duffing oscillator using variable order variable stepsize block method |
| url | http://psasir.upm.edu.my/id/eprint/64097/1/Solution%20for%20nonlinear%20Duffing%20oscillator%20using%20variable%20order%20variable%20stepsize%20block%20method.pdf |
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