Solution to the one-dimensional Rayleigh-Plesset equation by the Differential Transform method
Aneet Dharmavaram Narendranath
TL;DR
This paper applies the differential transform method to find a series solution for the one-dimensional Rayleigh-Plesset equation, demonstrating its potential for solving nonlinear differential equations.
Contribution
It introduces the use of the differential transform method for solving the one-dimensional Rayleigh-Plesset equation for the first time.
Findings
Series solution obtained for the RPE
Demonstrates effectiveness of DTM for nonlinear equations
Provides initial validation of DTM in bubble dynamics
Abstract
The differential transform method (DTM) is a relatively new technique that may be used to find a series solution to differential equations (both linear and nonlinear) through an iterative process. This brief manuscript is an initial effort in applying the DTM to provide a series solution to the one-dimensional Rayleigh-Plesset equation (RPE).
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Taxonomy
TopicsDifferential Equations and Numerical Methods · Fluid Dynamics and Thin Films · Numerical methods for differential equations