Author(s)

Moeiz Rouis, Khaled Omrani

Institut Supérieur des Sciences Appliquées et de Technologie de Sousse, Sousse, Tunisia.

In this paper, a linearized three level difference scheme is derived for two-dimensional model of an alloy solidification problem called Sivashinsky equation. Further, it is proved that the scheme is uniquely solvable and convergent with convergence rate of order two in a discrete L^∞-norm. At last, numerical experiments are carried out to support the theoretical claims.

Solidification Problem, Sivashinsky Equation, Linearized Difference Scheme, Solvability, Convergence

Rouis, M. and Omrani, K. (2016) On The Numerical Solution of Two Dimensional Model of an Alloy Solidification Problem. Modeling and Numerical Simulation of Material Science, 6, 1-9. doi: 10.4236/mnsms.2016.61001.