Sun, Z.Z. (2005) Numerical Methods of the Partial Differential Equations. Sciences Press, Beijing.

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.