## Abstract

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.

## Authors

C. I. **Gheorghiu**

-Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

C. **Morosanu**

-Alexandru Ioan Cuza University Iasi

## Keywords

## Cite this paper as:

C.I. Gheorghiu, C. Morosanu, *Accurate spectral solutions to a phase-field transition system*, ROMAI J., **10** (2014) 2, 1-11.

### References

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## About this paper

##### Journal

ROMAI J.

##### Publisher Name

Editions de l’Academie Roumaine

##### DOI

##### Print ISSN

1841-5512

##### Online ISSN

2065-7714

## MR

?

## ZBL

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