The Method of Lines and Invariant Imbedding for Elliptic and Parabolic Free Boundary Problems

A combination of the method of lines and invariant imbedding is suggested as a general purpose numerical algorithm for free boundary problems. Its effectiveness is illustrated by computing the solidification of a binary alloy in one dimension, electrochemical machining and Hele–Shaw flow in two dimensions, and a Stefan and ablation problem in three dimensions.