ON A VARIABLE TIME-STEP METHOD FOR THE ONE-DIMENSIONAL STEFAN PROBLEM

Several variable time-step (VTS) methods have been suggested by various authors for the solution of the one-dimensional Stefan problem. All of these methods involve an iterative computation of the time-step for a given advancement of the moving boundary. During each iteration, a linear system of equations needs to be solved. Some modifications of an existing VTS method due to R.S. Gupta and D. Kumar are presented. The modifications include the use of a tridiagonal solution of the linear system involved instead of Gaussian elimination and the use of an integral relationship to improve the time step instead of a difference formula. The first modification yields increased efficiency while the second results in increased accuracy. Numerical results are presented for two problems.