Numerical integration methods in gas-bubble dynamics

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Abstract
A recent detailed formulation of the dynamics of a gas bubble requires the numerical integration of a nonlinear heat equation in the bubble. In this article, a variety of numerical methods for this purpose are studied. The most efficient technique is found to be an adaptive Galerkin–Chebyshev spectral method, which is explained in detail. Examples of oscillations at high forcing and chaotic response are also given. These results differ very considerably from those obtained by use of the simpler models used by previous investigators.

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