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Volume 25, Issue 3
Finding Periodic Solutions of High Order Duffing Equations via Homotopy Method

Xue Yang & Xu Xu

Commun. Math. Res., 25 (2009), pp. 193-203.

Published online: 2021-07

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  • Abstract

This paper presents a detailed analysis of finding the periodic solutions for the high order Duffing equation $$x^{(2n)} + g(x) = e(t)   (n≥1).$$Firstly, we give a constructive proof for the existence of periodic solutions via the homotopy method. Then we establish an efficient and global convergence method to find periodic solutions numerically.

  • Keywords

high order Duffing equation, periodic solution, homotopy method.

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COPYRIGHT: © Global Science Press

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@Article{CMR-25-193, author = {Yang , Xue and Xu , Xu}, title = {Finding Periodic Solutions of High Order Duffing Equations via Homotopy Method}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {25}, number = {3}, pages = {193--203}, abstract = {

This paper presents a detailed analysis of finding the periodic solutions for the high order Duffing equation $$x^{(2n)} + g(x) = e(t)   (n≥1).$$Firstly, we give a constructive proof for the existence of periodic solutions via the homotopy method. Then we establish an efficient and global convergence method to find periodic solutions numerically.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19326.html} }
TY - JOUR T1 - Finding Periodic Solutions of High Order Duffing Equations via Homotopy Method AU - Yang , Xue AU - Xu , Xu JO - Communications in Mathematical Research VL - 3 SP - 193 EP - 203 PY - 2021 DA - 2021/07 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19326.html KW - high order Duffing equation, periodic solution, homotopy method. AB -

This paper presents a detailed analysis of finding the periodic solutions for the high order Duffing equation $$x^{(2n)} + g(x) = e(t)   (n≥1).$$Firstly, we give a constructive proof for the existence of periodic solutions via the homotopy method. Then we establish an efficient and global convergence method to find periodic solutions numerically.

Yang , Xue and Xu , Xu. (2021). Finding Periodic Solutions of High Order Duffing Equations via Homotopy Method. Communications in Mathematical Research . 25 (3). 193-203. doi:
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