Universidad Nacional de Colombia, Fizmako Research Group, Bogota, Colombia.
ScientificWorldJournal. 2022 May 17;2022:2357258. doi: 10.1155/2022/2357258. eCollection 2022.
In this work, we study the Duffing equation. Analytical solution for undamped and unforced case is provided for any given arbitrary initial conditions. An approximate analytical solution is given for the damped or trigonometrically forced Duffing equation for arbitrary initial conditions. The analytical solutions are expressed in terms of elementary trigonometric functions as well as in terms of the Jacobian elliptic functions. Examples are added to illustrate the obtained results. We also introduce new functions for approximating the Jacobian and Weierstrass elliptic functions in terms of the trigonometric functions sine and cosine. Results are high accurate.
在这项工作中，我们研究了杜芬方程。对于任何给定的任意初始条件，都给出了无阻尼和无外力情况下的解析解。对于任意初始条件的阻尼或三角函数强迫杜芬方程，给出了近似解析解。解析解表示为基本三角函数以及雅可比椭圆函数。添加了示例来说明获得的结果。我们还引入了新的函数，以便根据正弦和余弦三角函数来近似雅可比和魏尔斯特拉斯椭圆函数。结果是高度精确的。
