On The Numerical Solution of Two Dimensional Model of an Alloy Solidification Problem

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.