Numerical solution of a free boundary problem by continuation

An algorithm is described for the numerical solution of a free boundary problem using continuation. The problem considered is a quasi-steady problem arising in electrochemical machining. The domain of the problem is mapped onto a square and the governing nonlinear equations are discretised using finite differences. A Newton-like iteration is employed for the solution of the nonlinear algebraic system and global convergence is achieved by means of continuation. Numerical results are included.