Homotopy Analysis Method for the Rayleigh Equation Governing the Radial Dynamics of a Multielectron Bubble

Figure 8

Comparison between 4th-order HAM solutions (hollow symbols) and Runge-Kutta numerical solutions (solid lines) for: 𝑥(𝜏), 𝑥^(𝜏) and 𝑥^(𝜏) at different values of 𝛽. (a) 𝛼=1, 𝛽=0.443495 (𝑝=300 Pa), 𝜃=1, 𝑎=1.00002, ℎ=−1.4; (b) 𝛼=1, 𝛽=1.47832 (𝑝=1000 Pa), 𝜃=1, 𝑎=1.00002, ℎ=−1.7. All parameter values are for a MEB containing 10⁴ electrons with an equilibrium radius 𝑅_𝑐=1.06441 μm.

(a)

(b)