On the finite differences schemes for the numerical solution of two-dimensional moving boundary problem

In this paper, two different finite differences schemes are presented for numerical solution of two-dimensional moving boundary problem. The methods are illustrated by solving sample problem in two-dimensional solidification of the square prism. The finite difference schemes developed for this purpose are based on the method of lines using interpolation polynomials. The fully explicit method developed here which has reasonable accuracy, and Peaceman and Rachford alternating direction implicit (ADI) formula illustrated by solving sample problem. The accuracies of the resulting methods are verified by numerical testing. The numerical results are obtained by present methods are compared with earlier authors. 2004 Elsevier Inc. All rights reserved.