TITLE:
On The Numerical Solution of Two Dimensional Model of an Alloy Solidification Problem
AUTHORS:
Moeiz Rouis, Khaled Omrani
KEYWORDS:
Solidification Problem, Sivashinsky Equation, Linearized Difference Scheme, Solvability, Convergence
JOURNAL NAME:
Modeling and Numerical Simulation of Material Science,
Vol.6 No.1,
January
28,
2016
ABSTRACT: 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.