abstract
- © Published under licence by IOP Publishing Ltd.This work establishes a sufficient condition for convergence of a semi-implicit finite difference scheme with variable space grid of fourth order of accuracy in space, previously set by the authors. The scheme is intended to solve one-dimensional two-phase Stefan problems. The proofs of the above-mentioned results are based on estimates which are obtained and subsequently employed in order to find an upper bound of the discretization error both at phases and the interface. The computational behavior of the scheme under the sufficient condition is corroborated by a series of numerical tests.