Analytical and Numerical Study on Forced and Damped Complex Duffing Oscillators
In this work, some general forms for forced and damped complex Duffing oscillators (FDCDOs), including two different models, which are known as the forced and damped complex Duffing oscillator (I) (FDCDO (I)) and FDCDO (II), are investigated by using some effective analytical and numerical approache...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/23/4475 |
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| author | Weaam Alhejaili Alvaro H. Salas Samir A. El-Tantawy |
| author_facet | Weaam Alhejaili Alvaro H. Salas Samir A. El-Tantawy |
| author_sort | Weaam Alhejaili |
| collection | DOAJ |
| description | In this work, some general forms for forced and damped complex Duffing oscillators (FDCDOs), including two different models, which are known as the forced and damped complex Duffing oscillator (I) (FDCDO (I)) and FDCDO (II), are investigated by using some effective analytical and numerical approaches. For the analytical approximation, the two models of the FDCDOs are reduced to two decoupled standard forced and damped Duffing oscillators (FDDOs). After that, both the ansatz method and Krylov–Bogoliubov–Mitropolsky (KBM) approach are applied in order to derive some accurate analytical approximations in terms of trigonometric functions. For the numerical approximations, the finite difference method is employed to analyze the two coupled models without causing them to be decoupled for the original problems. In addition, all obtained analytical and numerical approximations are compared with the fourth-order Runge–Kutta (RK4) numerical approximations. Moreover, the maximum residual distance error (MRDE) is estimated in order to verify the accuracy of all obtained approximations. |
| first_indexed | 2024-03-09T17:40:46Z |
| format | Article |
| id | doaj.art-7ae76ffcba704ceb974ee8a767eefe0b |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T17:40:46Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-7ae76ffcba704ceb974ee8a767eefe0b2023-11-24T11:34:12ZengMDPI AGMathematics2227-73902022-11-011023447510.3390/math10234475Analytical and Numerical Study on Forced and Damped Complex Duffing OscillatorsWeaam Alhejaili0Alvaro H. Salas1Samir A. El-Tantawy2Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaFIZMAKO Research Group, Department of Mathematics and Statistics, Universidad Nacional de Colombia, Manizales 170001, ColombiaDepartment of Physics, Faculty of Science, Port Said University, Port Said 42521, EgyptIn this work, some general forms for forced and damped complex Duffing oscillators (FDCDOs), including two different models, which are known as the forced and damped complex Duffing oscillator (I) (FDCDO (I)) and FDCDO (II), are investigated by using some effective analytical and numerical approaches. For the analytical approximation, the two models of the FDCDOs are reduced to two decoupled standard forced and damped Duffing oscillators (FDDOs). After that, both the ansatz method and Krylov–Bogoliubov–Mitropolsky (KBM) approach are applied in order to derive some accurate analytical approximations in terms of trigonometric functions. For the numerical approximations, the finite difference method is employed to analyze the two coupled models without causing them to be decoupled for the original problems. In addition, all obtained analytical and numerical approximations are compared with the fourth-order Runge–Kutta (RK4) numerical approximations. Moreover, the maximum residual distance error (MRDE) is estimated in order to verify the accuracy of all obtained approximations.https://www.mdpi.com/2227-7390/10/23/4475complex Duffing oscillatorsdamped complex oscillatorforced and damped complex oscillatortrigonometric functionsKBM methodansatz method |
| spellingShingle | Weaam Alhejaili Alvaro H. Salas Samir A. El-Tantawy Analytical and Numerical Study on Forced and Damped Complex Duffing Oscillators Mathematics complex Duffing oscillators damped complex oscillator forced and damped complex oscillator trigonometric functions KBM method ansatz method |
| title | Analytical and Numerical Study on Forced and Damped Complex Duffing Oscillators |
| title_full | Analytical and Numerical Study on Forced and Damped Complex Duffing Oscillators |
| title_fullStr | Analytical and Numerical Study on Forced and Damped Complex Duffing Oscillators |
| title_full_unstemmed | Analytical and Numerical Study on Forced and Damped Complex Duffing Oscillators |
| title_short | Analytical and Numerical Study on Forced and Damped Complex Duffing Oscillators |
| title_sort | analytical and numerical study on forced and damped complex duffing oscillators |
| topic | complex Duffing oscillators damped complex oscillator forced and damped complex oscillator trigonometric functions KBM method ansatz method |
| url | https://www.mdpi.com/2227-7390/10/23/4475 |
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