Numerical Solving Of A Free Boundary Phase Field Model Using Krylov Subspace Method

Mathematics Research Report MRR95-066

Numerical Solving Of A Free Boundary Phase Field Model Using Krylov Subspace Method

Teresa Leyk and Stephen G. Roberts

Abstract: We consider the numerical methods for solving a free boundary problem arising from the phase transition. The boundary in the problem is assumed to have a finite thickness. The phenomena is described by a coupled pair of nonlinear parabolic differential equations. To get a numerical solution the Krylov subspace method is applied. (The Krylov subspace method is described in the paper [E. Gallopoulos and Y. Saad].) The Krylov subspace method is competitive with the standard explicit Euler method and the Crank-Nicolson method.

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