On the Analytical Solutions of the Forced Damping Duffing Equation in the Form of Weierstrass Elliptic Function and its Applications

<div>The comparison between the analytical solution (<a href="https://static.hindawi.com/articles/mpe/volume-2021/6678102/figures/#EEq20">20</a>) (dotted curve) and the RK4 numerical solution (dashed curve) for the forced undamping Duffing equation (<a href="https://static.hindawi.com/articles/mpe/volume-2021/6678102/figures/#EEq21">21</a>) is investigated for <span class="nowrap"><svg height="12.7178pt" id="M56" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 118.512 12.7178" width="118.512pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M478 372C478 418 458 448 431 448C409 448 389 431 389 410C389 404 391 400 394 395C398 388 406 371 406 348C406 253 308 122 251 51H249C254 122 249 257 231 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Mathematical Problems in Engineering

fig1

Figure 1

Figure 1: On the Analytical Solutions of the Forced Damping Duffing Equation in the Form of Weierstrass Elliptic Function and its Applications 