An Approximate Optimization Method for Solving Stiff Ordinary Differential Equations With Combinational Mutation Strategy of Differential Evolution Algorithm
This paper examines the implementation of simple combination mutation of differential evolution algorithm for solving stiff ordinary differential equations. We use the weighted residual method with a series expansion to approximate the solutions of stiff ordinary differential equations. We solve th...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Brno University of Technology
2022-12-01
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| Series: | Mendel |
| Subjects: | |
| Online Access: | https://mendel-journal.org/index.php/mendel/article/view/196 |
| _version_ | 1811301482006315008 |
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| author | Werry Febrianti Kuntjoro Adji Sidarto Novriana Sumarti |
| author_facet | Werry Febrianti Kuntjoro Adji Sidarto Novriana Sumarti |
| author_sort | Werry Febrianti |
| collection | DOAJ |
| description |
This paper examines the implementation of simple combination mutation of differential evolution algorithm for solving stiff ordinary differential equations. We use the weighted residual method with a series expansion to approximate the solutions of stiff ordinary differential equations. We solve the problems from an ordinary stiff differential equation for linear and nonlinear problems. Then, we also implement our method for solving stiff systems of ordinary differential equations. We find that our algorithm can approximate the exact solution of a stiff ordinary differential equation with the smallest error for each length of series that we have chosen. Thus, this approximation method, by using the optimization method of simple combination differential evolution, can be a good tool for solving stiff ordinary differential equations.
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| first_indexed | 2024-04-13T07:09:38Z |
| format | Article |
| id | doaj.art-f6594c70847e4b9b9d7f9da5ca0c0d6e |
| institution | Directory Open Access Journal |
| issn | 1803-3814 2571-3701 |
| language | English |
| last_indexed | 2024-04-13T07:09:38Z |
| publishDate | 2022-12-01 |
| publisher | Brno University of Technology |
| record_format | Article |
| series | Mendel |
| spelling | doaj.art-f6594c70847e4b9b9d7f9da5ca0c0d6e2022-12-22T02:56:55ZengBrno University of TechnologyMendel1803-38142571-37012022-12-0128210.13164/mendel.2022.2.054An Approximate Optimization Method for Solving Stiff Ordinary Differential Equations With Combinational Mutation Strategy of Differential Evolution AlgorithmWerry Febrianti0Kuntjoro Adji Sidarto1Novriana Sumarti2Departmen Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi BandungDepartmen Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi BandungDepartmen Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung This paper examines the implementation of simple combination mutation of differential evolution algorithm for solving stiff ordinary differential equations. We use the weighted residual method with a series expansion to approximate the solutions of stiff ordinary differential equations. We solve the problems from an ordinary stiff differential equation for linear and nonlinear problems. Then, we also implement our method for solving stiff systems of ordinary differential equations. We find that our algorithm can approximate the exact solution of a stiff ordinary differential equation with the smallest error for each length of series that we have chosen. Thus, this approximation method, by using the optimization method of simple combination differential evolution, can be a good tool for solving stiff ordinary differential equations. https://mendel-journal.org/index.php/mendel/article/view/196Stiff ordinary differential equationFourier seriesWeighted residual methodSimple combination mutation of differential evolution |
| spellingShingle | Werry Febrianti Kuntjoro Adji Sidarto Novriana Sumarti An Approximate Optimization Method for Solving Stiff Ordinary Differential Equations With Combinational Mutation Strategy of Differential Evolution Algorithm Mendel Stiff ordinary differential equation Fourier series Weighted residual method Simple combination mutation of differential evolution |
| title | An Approximate Optimization Method for Solving Stiff Ordinary Differential Equations With Combinational Mutation Strategy of Differential Evolution Algorithm |
| title_full | An Approximate Optimization Method for Solving Stiff Ordinary Differential Equations With Combinational Mutation Strategy of Differential Evolution Algorithm |
| title_fullStr | An Approximate Optimization Method for Solving Stiff Ordinary Differential Equations With Combinational Mutation Strategy of Differential Evolution Algorithm |
| title_full_unstemmed | An Approximate Optimization Method for Solving Stiff Ordinary Differential Equations With Combinational Mutation Strategy of Differential Evolution Algorithm |
| title_short | An Approximate Optimization Method for Solving Stiff Ordinary Differential Equations With Combinational Mutation Strategy of Differential Evolution Algorithm |
| title_sort | approximate optimization method for solving stiff ordinary differential equations with combinational mutation strategy of differential evolution algorithm |
| topic | Stiff ordinary differential equation Fourier series Weighted residual method Simple combination mutation of differential evolution |
| url | https://mendel-journal.org/index.php/mendel/article/view/196 |
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