Scaling Invariance and the Iterative Transformation Method for a Class of Parabolic Moving Boundary Problems
Provides a numerical method for solving a class of moving boundary problems, but the contribution is incremental as it applies existing scaling invariance theory and iterative transformation method to new examples.
The authors apply scaling invariance analysis to reduce parabolic moving boundary problems to ODE-governed free boundary problems, and solve them with an iterative transformation method. Numerical results for two example problems match exact or approximate solutions well.
In this paper we apply a scaling invariance analysis to reduce a class of parabolic moving boundary problems to free boundary problems governed by ordinary differential equations. As well known free boundary problems are always non-linear and, consequently, their numerical solution is often obtained iteratively. Among the numerical methods, developed for the numerical solution of this kind of problems, we focus on the iterative transformation method that has been defined within scaling invariance theory. Then, as illustrative examples, we solve two problems of interest in the applications. The obtained numerical results are found in good agreement with exact or approximate ones.