Research Article

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

Figure 7

(a) Comparison between 5th-order HAM solution (hollow symbols) and Runge-Kutta numerical solution (solid lines) of 𝑟 ( 𝜏 ) for different values of 𝜃 with the following fixed values: 𝜉 = 1 . 1 5 , 𝛼 = 1 , = 2 . 3 . Square symbols: 𝑍 = 1 0 electrons, 𝑅 𝑐 = 1 2 5  Å and 𝜃 = 0 . 6 1 7 4 0 5 ; triangular symbols: for 𝑍 = 1 0 0 electrons, 𝑅 𝑐 = 5 2 5  Å and 𝜃 = 0 . 8 3 3 3 4 ; diamond symbols: for 𝑍 = 1 0 4 electrons, 𝑅 𝑐 = 1 . 0 6 4 𝜇 m and 𝜃 = 0 . 9 9 9 9 3 9 ; circular symbol: for 𝑍 = 1 0 8 electrons, 𝑅 𝑐 = 4 8 6 𝜇 m and 𝜃 = 1 . 0 5 0 4 9 . (b) Effect of varying the dimensionless initial radius 𝜉 . Comparison between 5th-order HAM solution (hollow symbols) and Runge-Kutta numerical solution (solid lines) for 𝑟 ( 𝜏 ) with: 𝜉 = 1 . 2 and = 1 . 3 6 (square symbols), 𝜉 = 1 . 3 and = 1 . 2 5 (circular symbols), 𝜉 = 1 . 4 and = 0 . 9 7 (triangular symbols). The remaining parameters are set to: 𝛼 = 1 , 𝜃 = 0 . 9 9 9 9 3 9 .
591058.fig.007a
(a)
591058.fig.007b
(b)