A two-stage, two-level finite difference scheme for moving boundary problems

Abstract A two-stage, two-level finite difference scheme is devised which, after applying a coordinate transformation, requires only a single iteration of a modified Newton method to produce second-order approximations to the solution of nonlinear parabolic moving boundary problems. Numerical evidence of unconditional stability and second-order convergence (in space and time) to both the solution and the moving boundary is presented for two particular problems. The proposed scheme is expected to be competitive with most current ‘front tracking’ methods.