Numerical solution of full fractional Duffing equations with Cubic-Quintic-Heptic nonlinearities
| Autor: | A. H. Refahi Sheikhani, H. Saberi Najafi, Ali Abdolahzadeh Ziabari, P. Pirmohabbati |
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| Rok vydání: | 2020 |
| Předmět: |
nonlinear oscillator
lcsh:Mathematics General Mathematics duffing differential equation Order (ring theory) Derivative block-pulse functions lcsh:QA1-939 fractional order Quintic function Fractional calculus Matrix (mathematics) Nonlinear system Wavelet cubic-quintic-heptic Applied mathematics Restoring force Mathematics |
| Zdroj: | AIMS Mathematics, Vol 5, Iss 2, Pp 1621-1641 (2020) |
| ISSN: | 2473-6988 |
| DOI: | 10.3934/math.2020110 |
| Popis: | In this article, based on the operational matrix of fractional order integration, we introduce a method for the numerical solution of fractional strongly nonlinear Duffing oscillators with cubic-quintic-heptic nonlinear restoring force and then use it in some cases. For this purpose, concerning the Caputo sense, we implement the block-pulse wavelets matrix of fractional order integration. To reach this aim, we analyse the errors. The approach has been examined by some numerical examples and changes in coefficients as well as in the derivative of the equation too. It is shown that this method works well for all the parameters and order of the fractional derivative. Results indicate the precision and computational performance of the suggested algorithm. |
| Databáze: | OpenAIRE |
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