Omrani, K. (2003) A Second-Order Splitting Method for a Finite Difference Scheme for the Sivashinsky Equation. Applied Mathematics Letters, 16, 441-445.
http://dx.doi.org/10.1016/S0893-9659(03)80070-8

has been cited by the following article:

• 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.