Method of lines and runge-kutta method in solving partial differential equation for heat equation
Solving the differential equation for Newton’s cooling law mostly consists of several fragments formed during a long time to solve the equation. However, the stiff type problems seem cannot be solved efficiently via some of these methods. This research will try to overcome such problems and compare...
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| Language: | en |
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FAZ Publishing
2021
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| Online Access: | http://eprints.uthm.edu.my/2702/1/J12439_7f876ce4db2c61f8e4bd8dd0e0aa4b62.pdf http://eprints.uthm.edu.my/2702/ |
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| author | Manshoor, Bukhari Salleh, Hamidon Khalid, Amir Sayed Abdelaal, Muhammed Abdelfattah |
| author_facet | Manshoor, Bukhari Salleh, Hamidon Khalid, Amir Sayed Abdelaal, Muhammed Abdelfattah |
| author_sort | Manshoor, Bukhari |
| building | UTHM Library |
| collection | Institutional Repository |
| content_provider | Universiti Tun Hussein Onn Malaysia |
| content_source | UTHM Institutional Repository |
| continent | Asia |
| country | Malaysia |
| description | Solving the differential equation for Newton’s cooling law mostly consists of several fragments formed during a long time to solve the equation. However, the stiff type problems seem cannot be solved efficiently via some of these methods. This research will try to overcome such problems and compare results from two classes of numerical methods for heat equation problems. The heat or diffusion equation, an example of parabolic equations, is classified into Partial Differential Equations. Two classes of numerical methods which are Method of Lines and Runge-Kutta will be performed and discussed. The development, analysis and implementation have been made using the Matlab language, which the graphs exhibited to highlight the accuracy and efficiency of the numerical methods. From the solution of the equations, it showed that better accuracy is achieved through the new combined method by Method of Lines and Runge-Kutta method. |
| format | Article |
| id | my.uthm.eprints-2702 |
| institution | Universiti Tun Hussein Onn Malaysia |
| language | en |
| publishDate | 2021 |
| publisher | FAZ Publishing |
| record_format | eprints |
| spelling | my.uthm.eprints-27022021-10-31T04:49:15Z http://eprints.uthm.edu.my/2702/ Method of lines and runge-kutta method in solving partial differential equation for heat equation Manshoor, Bukhari Salleh, Hamidon Khalid, Amir Sayed Abdelaal, Muhammed Abdelfattah QA299.6-433 Analysis Solving the differential equation for Newton’s cooling law mostly consists of several fragments formed during a long time to solve the equation. However, the stiff type problems seem cannot be solved efficiently via some of these methods. This research will try to overcome such problems and compare results from two classes of numerical methods for heat equation problems. The heat or diffusion equation, an example of parabolic equations, is classified into Partial Differential Equations. Two classes of numerical methods which are Method of Lines and Runge-Kutta will be performed and discussed. The development, analysis and implementation have been made using the Matlab language, which the graphs exhibited to highlight the accuracy and efficiency of the numerical methods. From the solution of the equations, it showed that better accuracy is achieved through the new combined method by Method of Lines and Runge-Kutta method. FAZ Publishing 2021 Article PeerReviewed text en http://eprints.uthm.edu.my/2702/1/J12439_7f876ce4db2c61f8e4bd8dd0e0aa4b62.pdf Manshoor, Bukhari and Salleh, Hamidon and Khalid, Amir and Sayed Abdelaal, Muhammed Abdelfattah (2021) Method of lines and runge-kutta method in solving partial differential equation for heat equation. Journal of Complex Flow, 3 (1). pp. 21-25. |
| spellingShingle | QA299.6-433 Analysis Manshoor, Bukhari Salleh, Hamidon Khalid, Amir Sayed Abdelaal, Muhammed Abdelfattah Method of lines and runge-kutta method in solving partial differential equation for heat equation |
| title | Method of lines and runge-kutta method in solving partial differential equation for heat equation |
| title_full | Method of lines and runge-kutta method in solving partial differential equation for heat equation |
| title_fullStr | Method of lines and runge-kutta method in solving partial differential equation for heat equation |
| title_full_unstemmed | Method of lines and runge-kutta method in solving partial differential equation for heat equation |
| title_short | Method of lines and runge-kutta method in solving partial differential equation for heat equation |
| title_sort | method of lines and runge-kutta method in solving partial differential equation for heat equation |
| topic | QA299.6-433 Analysis |
| url | http://eprints.uthm.edu.my/2702/1/J12439_7f876ce4db2c61f8e4bd8dd0e0aa4b62.pdf http://eprints.uthm.edu.my/2702/ |
| url_provider | http://eprints.uthm.edu.my/ |