%0 Journal Article
%T On The Numerical Solution of Two Dimensional Model of an Alloy  Solidification Problem
%A Moeiz Rouis
%A Khaled Omrani
%J Modeling and Numerical Simulation of Material Science
%P 1-9
%@ 2164-5353
%D 2016
%I Scientific Research Publishing
%R 10.4236/mnsms.2016.61001
%X 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<span style=\"font-size:6.5pt;font-family:&quot;color:#323E32;background:#D9D9D9;\"><sup>¡Þ</sup></span>-norm. At last, numerical experiments are carried out to support the theoretical claims.
%K Solidification Problem
%K Sivashinsky Equation
%K Linearized Difference Scheme
%K Solvability
%K Convergence
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=63120