Optimized hybrid block adams method for solving first order ordinary differential equations
Multistep integration methods are being extensively used in the simulations of high dimensional systems due to their lower computational cost. The block methods were developed with the intent of obtaining numerical results on numerous points at a time and improving computational efficiency. Hybrid b...
| Main Authors: | Soomro, H., Zainuddin, N., Daud, H., Sunday, J. |
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| Format: | Article |
| Institution: | Universiti Teknologi Petronas |
| Record Id / ISBN-0: | utp-eprints.33274 / |
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Tech Science Press
2022
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https://www.scopus.com/inward/record.uri?eid=2-s2.0-85127364332&doi=10.32604%2fcmc.2022.025933&partnerID=40&md5=e1105c7c084d9f4a2ecc74cc55aa3503 http://eprints.utp.edu.my/33274/ |
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utp-eprints.332742022-07-26T06:32:01Z Optimized hybrid block adams method for solving first order ordinary differential equations Soomro, H. Zainuddin, N. Daud, H. Sunday, J. Multistep integration methods are being extensively used in the simulations of high dimensional systems due to their lower computational cost. The block methods were developed with the intent of obtaining numerical results on numerous points at a time and improving computational efficiency. Hybrid block methods for instance are specifically used in numerical integration of initial value problems. In this paper, an optimized hybrid block Adams block method is designed for the solutions of linear and nonlinear first-order initial value problems in ordinary differential equations (ODEs). In deriving themethod, the Lagrange interpolation polynomial was employed based on some data points to replace the differential equation function and it was integrated over a specified interval. Furthermore, the convergence properties along with the region of stability of the method were examined. It was concluded that the newly derived method is convergent, consistent, and zero-stable. The method was also found to be A-stable implying that it covers the whole of the left/negative half plane. From the numerical computations of absolute errors carried out using the newly derived method, it was found that the method performed better than the ones with which we compared our results with. Themethod also showed its superiority over the existing methods in terms of stability and convergence. © 2022 Tech Science Press. All rights reserved. Tech Science Press 2022 Article NonPeerReviewed https://www.scopus.com/inward/record.uri?eid=2-s2.0-85127364332&doi=10.32604%2fcmc.2022.025933&partnerID=40&md5=e1105c7c084d9f4a2ecc74cc55aa3503 Soomro, H. and Zainuddin, N. and Daud, H. and Sunday, J. (2022) Optimized hybrid block adams method for solving first order ordinary differential equations. Computers, Materials and Continua, 72 (2). pp. 2947-2961. http://eprints.utp.edu.my/33274/ |
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Universiti Teknologi Petronas |
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Multistep integration methods are being extensively used in the simulations of high dimensional systems due to their lower computational cost. The block methods were developed with the intent of obtaining numerical results on numerous points at a time and improving computational efficiency. Hybrid block methods for instance are specifically used in numerical integration of initial value problems. In this paper, an optimized hybrid block Adams block method is designed for the solutions of linear and nonlinear first-order initial value problems in ordinary differential equations (ODEs). In deriving themethod, the Lagrange interpolation polynomial was employed based on some data points to replace the differential equation function and it was integrated over a specified interval. Furthermore, the convergence properties along with the region of stability of the method were examined. It was concluded that the newly derived method is convergent, consistent, and zero-stable. The method was also found to be A-stable implying that it covers the whole of the left/negative half plane. From the numerical computations of absolute errors carried out using the newly derived method, it was found that the method performed better than the ones with which we compared our results with. Themethod also showed its superiority over the existing methods in terms of stability and convergence. © 2022 Tech Science Press. All rights reserved. |
| format |
Article |
| author |
Soomro, H. Zainuddin, N. Daud, H. Sunday, J. |
| spellingShingle |
Soomro, H. Zainuddin, N. Daud, H. Sunday, J. Optimized hybrid block adams method for solving first order ordinary differential equations |
| author_sort |
Soomro, H. |
| title |
Optimized hybrid block adams method for solving first order ordinary differential equations |
| title_short |
Optimized hybrid block adams method for solving first order ordinary differential equations |
| title_full |
Optimized hybrid block adams method for solving first order ordinary differential equations |
| title_fullStr |
Optimized hybrid block adams method for solving first order ordinary differential equations |
| title_full_unstemmed |
Optimized hybrid block adams method for solving first order ordinary differential equations |
| title_sort |
optimized hybrid block adams method for solving first order ordinary differential equations |
| publisher |
Tech Science Press |
| publishDate |
2022 |
| url |
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85127364332&doi=10.32604%2fcmc.2022.025933&partnerID=40&md5=e1105c7c084d9f4a2ecc74cc55aa3503 http://eprints.utp.edu.my/33274/ |
| _version_ |
1741197828855693312 |
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11.62408 |