The performance evaluation of chaotic maps in estimating the shape parameters of radial basis functions to solve partial differential equations
Purpose: This study aims to investigate the potential of chaotic optimization algorithms in improving performance compared to other optimization methods, focusing on determining the appropriate shape parameter of radial basis functions for solving partial differential equations.Methodology: In this...
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| Format: | Article |
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Ayandegan Institute of Higher Education, Tonekabon,
2024-06-01
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| Series: | تصمیم گیری و تحقیق در عملیات |
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| Online Access: | https://www.journal-dmor.ir/article_195562_c47b446eabdeadb4302fb7d22d1665bb.pdf |
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| _version_ | 1832577786138591232 |
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| author | Javad Alikhani Koupaei Mohammad Javad Ebadi Majid Iran Pour |
| author_facet | Javad Alikhani Koupaei Mohammad Javad Ebadi Majid Iran Pour |
| author_sort | Javad Alikhani Koupaei |
| collection | DOAJ |
| description | Purpose: This study aims to investigate the potential of chaotic optimization algorithms in improving performance compared to other optimization methods, focusing on determining the appropriate shape parameter of radial basis functions for solving partial differential equations.Methodology: In this research, a two-stage process is employed where the Kansa method, based on meshless local techniques, is combined with the FCW method. In the first stage, the FCW algorithm is utilized to obtain the optimal shape parameter for radial basis functions, followed by the Kansa method in the second stage to estimate the Root Mean Square (RMS) error for approximate solutions.Findings: Numerical results indicate that approximately 95% of the results obtained from two partial differential equations using PSO and FCW algorithms are similar. These results demonstrate the effectiveness and efficiency of this approach in estimating appropriate shape parameters for solving differential equations.Originality/Value: This study confirms the importance of chaos-based optimization algorithms in solving partial differential equations, which can contribute to future research in this field. |
| format | Article |
| id | doaj-art-04f7e1d2f122455788f1034565756dab |
| institution | Kabale University |
| issn | 2538-5097 2676-6159 |
| language | fas |
| publishDate | 2024-06-01 |
| publisher | Ayandegan Institute of Higher Education, Tonekabon, |
| record_format | Article |
| series | تصمیم گیری و تحقیق در عملیات |
| spelling | doaj-art-04f7e1d2f122455788f1034565756dab2025-01-30T15:03:40ZfasAyandegan Institute of Higher Education, Tonekabon,تصمیم گیری و تحقیق در عملیات2538-50972676-61592024-06-019119420510.22105/dmor.2024.424950.1806195562The performance evaluation of chaotic maps in estimating the shape parameters of radial basis functions to solve partial differential equationsJavad Alikhani Koupaei0Mohammad Javad Ebadi1Majid Iran Pour2Department of Mathematics, Payame Noor University, Tehran, Iran.Department of Mathematics, Chabahar Maritime University, Chabahar, Iran.3 Department of Computer Engineering and IT, Payam Noor University, Tehran, Iran.Purpose: This study aims to investigate the potential of chaotic optimization algorithms in improving performance compared to other optimization methods, focusing on determining the appropriate shape parameter of radial basis functions for solving partial differential equations.Methodology: In this research, a two-stage process is employed where the Kansa method, based on meshless local techniques, is combined with the FCW method. In the first stage, the FCW algorithm is utilized to obtain the optimal shape parameter for radial basis functions, followed by the Kansa method in the second stage to estimate the Root Mean Square (RMS) error for approximate solutions.Findings: Numerical results indicate that approximately 95% of the results obtained from two partial differential equations using PSO and FCW algorithms are similar. These results demonstrate the effectiveness and efficiency of this approach in estimating appropriate shape parameters for solving differential equations.Originality/Value: This study confirms the importance of chaos-based optimization algorithms in solving partial differential equations, which can contribute to future research in this field.https://www.journal-dmor.ir/article_195562_c47b446eabdeadb4302fb7d22d1665bb.pdfchaos optimization algorithmsradial basis functionskanza methodpartial differential equationsfirst carrier wave method |
| spellingShingle | Javad Alikhani Koupaei Mohammad Javad Ebadi Majid Iran Pour The performance evaluation of chaotic maps in estimating the shape parameters of radial basis functions to solve partial differential equations تصمیم گیری و تحقیق در عملیات chaos optimization algorithms radial basis functions kanza method partial differential equations first carrier wave method |
| title | The performance evaluation of chaotic maps in estimating the shape parameters of radial basis functions to solve partial differential equations |
| title_full | The performance evaluation of chaotic maps in estimating the shape parameters of radial basis functions to solve partial differential equations |
| title_fullStr | The performance evaluation of chaotic maps in estimating the shape parameters of radial basis functions to solve partial differential equations |
| title_full_unstemmed | The performance evaluation of chaotic maps in estimating the shape parameters of radial basis functions to solve partial differential equations |
| title_short | The performance evaluation of chaotic maps in estimating the shape parameters of radial basis functions to solve partial differential equations |
| title_sort | performance evaluation of chaotic maps in estimating the shape parameters of radial basis functions to solve partial differential equations |
| topic | chaos optimization algorithms radial basis functions kanza method partial differential equations first carrier wave method |
| url | https://www.journal-dmor.ir/article_195562_c47b446eabdeadb4302fb7d22d1665bb.pdf |
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