Numerical Investigation of the Fractional-Order Liénard and Duffing Equations Arising in Oscillating Circuit Theory
In this article, we present the Jacobi spectral colocation method to solve the fractional model of Liénard and Duffing equations with the Liouville–Caputo fractional derivative. These equations are the generalization of the spring–mass system equation and describe the oscillating circuit. The main r...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2020-04-01
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| Series: | Frontiers in Physics |
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| Online Access: | https://www.frontiersin.org/article/10.3389/fphy.2020.00120/full |
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| author | Harendra Singh H. M. Srivastava H. M. Srivastava H. M. Srivastava |
| author_facet | Harendra Singh H. M. Srivastava H. M. Srivastava H. M. Srivastava |
| author_sort | Harendra Singh |
| collection | DOAJ |
| description | In this article, we present the Jacobi spectral colocation method to solve the fractional model of Liénard and Duffing equations with the Liouville–Caputo fractional derivative. These equations are the generalization of the spring–mass system equation and describe the oscillating circuit. The main reason for using this technique is high accuracy and low computational cost compared to some other methods. The main solution behaviors of these equations are due to fractional orders, which are explained graphically. The convergence analysis of the proposed method is also provided. A comparison is made between the exact and approximate solutions. |
| first_indexed | 2024-12-12T04:05:16Z |
| format | Article |
| id | doaj.art-cde5c21cba7b4cab8c3eb99828b74009 |
| institution | Directory Open Access Journal |
| issn | 2296-424X |
| language | English |
| last_indexed | 2024-12-12T04:05:16Z |
| publishDate | 2020-04-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj.art-cde5c21cba7b4cab8c3eb99828b740092022-12-22T00:38:47ZengFrontiers Media S.A.Frontiers in Physics2296-424X2020-04-01810.3389/fphy.2020.00120525983Numerical Investigation of the Fractional-Order Liénard and Duffing Equations Arising in Oscillating Circuit TheoryHarendra Singh0H. M. Srivastava1H. M. Srivastava2H. M. Srivastava3Department of Mathematics, Post Graduate College, Ghazipur, Ghazipur, IndiaDepartment of Mathematics and Statistics, University of Victoria, Victoria, BC, CanadaDepartment of Medical Research, China Medical University Hospital, China Medical University, Taichung, ChinaDepartment of Mathematics and Informatics, Azerbaijan University, Baku, AzerbaijanIn this article, we present the Jacobi spectral colocation method to solve the fractional model of Liénard and Duffing equations with the Liouville–Caputo fractional derivative. These equations are the generalization of the spring–mass system equation and describe the oscillating circuit. The main reason for using this technique is high accuracy and low computational cost compared to some other methods. The main solution behaviors of these equations are due to fractional orders, which are explained graphically. The convergence analysis of the proposed method is also provided. A comparison is made between the exact and approximate solutions.https://www.frontiersin.org/article/10.3389/fphy.2020.00120/fullfractional Liénard equationfractional Duffing equationspectral colocation methodJacobi polynomialsconvergence analysis |
| spellingShingle | Harendra Singh H. M. Srivastava H. M. Srivastava H. M. Srivastava Numerical Investigation of the Fractional-Order Liénard and Duffing Equations Arising in Oscillating Circuit Theory Frontiers in Physics fractional Liénard equation fractional Duffing equation spectral colocation method Jacobi polynomials convergence analysis |
| title | Numerical Investigation of the Fractional-Order Liénard and Duffing Equations Arising in Oscillating Circuit Theory |
| title_full | Numerical Investigation of the Fractional-Order Liénard and Duffing Equations Arising in Oscillating Circuit Theory |
| title_fullStr | Numerical Investigation of the Fractional-Order Liénard and Duffing Equations Arising in Oscillating Circuit Theory |
| title_full_unstemmed | Numerical Investigation of the Fractional-Order Liénard and Duffing Equations Arising in Oscillating Circuit Theory |
| title_short | Numerical Investigation of the Fractional-Order Liénard and Duffing Equations Arising in Oscillating Circuit Theory |
| title_sort | numerical investigation of the fractional order lienard and duffing equations arising in oscillating circuit theory |
| topic | fractional Liénard equation fractional Duffing equation spectral colocation method Jacobi polynomials convergence analysis |
| url | https://www.frontiersin.org/article/10.3389/fphy.2020.00120/full |
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