Numerical solution of Volterra Integro-Differential Equations by hybrid block with quadrature rules method
In this paper, the implementation of one-step hybrid block method with quadrature rules will be proposed for solving linear and non-linear rst order Volterra Integro-Di erential Equations (VIDEs) of the second kind. VIDEs have important applications in many branches of sciences and engineering, suc...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Universiti Putra Malaysia Press
2020
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| Online Access: | http://psasir.upm.edu.my/id/eprint/86934/ http://psasir.upm.edu.my/id/eprint/86934/1/1.%20Zanariah%20%26%20Razaei.pdf |
| _version_ | 1848860325099601920 |
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| author | Janodi, Mohd Razaie Abdul Majid, Zanariah Ismail, Fudziah Senu, Norazak |
| author_facet | Janodi, Mohd Razaie Abdul Majid, Zanariah Ismail, Fudziah Senu, Norazak |
| author_sort | Janodi, Mohd Razaie |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper, the implementation of one-step hybrid block method with quadrature rules will be proposed for solving linear and non-linear rst order Volterra Integro-Di erential Equations (VIDEs) of the second kind. VIDEs have important applications in many branches of sciences and engineering, such as analysing rhythmic biological data can be conducted by utilizing a curve tting technique based on solutions of the VIDEs. The formulation of the hybrid block method is based on the Lagrange interpolation polynomial. The approximation of the integral part in the VIDEs will be estimated using the quadrature rules. The proposed hybrid block method of order ve will compute the numerical solutions at two points simultaneously at each integration steps. The stability analysis such as order of the method, consistency, zero stable and stability region of the method are deliberated. The xed step size is used to generate the results and the code is written in C language. Numerical simulations are presented to show the e ciency and accuracy of the hybrid method when compared to the Runge-Kutta of order four and ve in terms of accuracy, total steps, and total function calls. |
| first_indexed | 2025-11-15T12:43:26Z |
| format | Article |
| id | upm-86934 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T12:43:26Z |
| publishDate | 2020 |
| publisher | Universiti Putra Malaysia Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-869342022-01-07T08:42:58Z http://psasir.upm.edu.my/id/eprint/86934/ Numerical solution of Volterra Integro-Differential Equations by hybrid block with quadrature rules method Janodi, Mohd Razaie Abdul Majid, Zanariah Ismail, Fudziah Senu, Norazak In this paper, the implementation of one-step hybrid block method with quadrature rules will be proposed for solving linear and non-linear rst order Volterra Integro-Di erential Equations (VIDEs) of the second kind. VIDEs have important applications in many branches of sciences and engineering, such as analysing rhythmic biological data can be conducted by utilizing a curve tting technique based on solutions of the VIDEs. The formulation of the hybrid block method is based on the Lagrange interpolation polynomial. The approximation of the integral part in the VIDEs will be estimated using the quadrature rules. The proposed hybrid block method of order ve will compute the numerical solutions at two points simultaneously at each integration steps. The stability analysis such as order of the method, consistency, zero stable and stability region of the method are deliberated. The xed step size is used to generate the results and the code is written in C language. Numerical simulations are presented to show the e ciency and accuracy of the hybrid method when compared to the Runge-Kutta of order four and ve in terms of accuracy, total steps, and total function calls. Universiti Putra Malaysia Press 2020 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/86934/1/1.%20Zanariah%20%26%20Razaei.pdf Janodi, Mohd Razaie and Abdul Majid, Zanariah and Ismail, Fudziah and Senu, Norazak (2020) Numerical solution of Volterra Integro-Differential Equations by hybrid block with quadrature rules method. Malaysian Journal of Mathematical Sciences, 14 (2). 191 - 208. ISSN 1823-8343; ESSN: 2289-750X https://einspem.upm.edu.my/journal/fullpaper/vol14-12May/1.%20Zanariah%20&%20Razaei.pdf |
| spellingShingle | Janodi, Mohd Razaie Abdul Majid, Zanariah Ismail, Fudziah Senu, Norazak Numerical solution of Volterra Integro-Differential Equations by hybrid block with quadrature rules method |
| title | Numerical solution of Volterra Integro-Differential Equations by hybrid block with quadrature rules method |
| title_full | Numerical solution of Volterra Integro-Differential Equations by hybrid block with quadrature rules method |
| title_fullStr | Numerical solution of Volterra Integro-Differential Equations by hybrid block with quadrature rules method |
| title_full_unstemmed | Numerical solution of Volterra Integro-Differential Equations by hybrid block with quadrature rules method |
| title_short | Numerical solution of Volterra Integro-Differential Equations by hybrid block with quadrature rules method |
| title_sort | numerical solution of volterra integro-differential equations by hybrid block with quadrature rules method |
| url | http://psasir.upm.edu.my/id/eprint/86934/ http://psasir.upm.edu.my/id/eprint/86934/ http://psasir.upm.edu.my/id/eprint/86934/1/1.%20Zanariah%20%26%20Razaei.pdf |