The paper is mainly concerned with numerical approximation of solutions to the phase-field transition system (Caginalp’s model), subject to the non-homogeneous Dirichlet boundary conditions. Numerical approximation of solutions to the nonlinear phase-field (Allen-Cahn) equation, supplied with the non-homogeneous Dirichlet boundary conditions as well as with homogeneous Cauchy-Neumann boundary conditions is also of interest. To achieve these goals, a Chebyshev collocation method, coupled with a Runge-Kutta scheme, has been used. The role of the nonlinearity and the influence of the boundary conditions on numerical approximation in allen-Cahn equation were analyzed too. To cope with the stiffness of Caginalp’s model, a multistep solver has been additionally used; all this, in order to march in time along with the same spatial discretization. Some numerical experiments are reported in order to illustrate the effectiveness of our numerical approach.
C. I. Gheorghiu
-Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy
-Alexandru Ioan Cuza University Iasi
C.I. Gheorghiu, C. Morosanu, Accurate spectral solutions to a phase-field transition system, ROMAI J., 10 (2014) 2, 1-11.
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