On The Numerical Solution of Two Dimensional Model of an Alloy Solidification Problem - Modeling and Numerical Simulation of Material Science

MNSMS > Vol.6 No.1, January 2016

Modeling and Numerical Simulation of Material Science

Volume 6, Issue 1 (January 2016)

ISSN Print: 2164-5345 ISSN Online: 2164-5353

Google-based Impact Factor: 0.7 Citations

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

HTML XML

Download as PDF (Size: 290KB) PP. 1-9

DOI: 10.4236/mnsms.2016.61001 3,360 Downloads 4,410 Views Citations

Author(s)

Moeiz Rouis, Khaled Omrani

Affiliation(s)

Institut Supérieur des Sciences Appliquées et de Technologie de Sousse, Sousse, Tunisia.

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.

KEYWORDS

Solidification Problem, Sivashinsky Equation, Linearized Difference Scheme, Solvability, Convergence

Share and Cite:

Rouis, M. and Omrani, K. (2016) On The Numerical Solution of Two Dimensional Model of an Alloy Solidification Problem. Modeling and Numerical Simulation of Material Science, 6, 1-9. doi: 10.4236/mnsms.2016.61001.

Cited by

[1]	High Accuracy Analysis of Nonconforming Mixed Finite Element Method for the Nonlinear Sivashinsky Equation
	2020

[2]	A class of two-and three-level implicit methods of order two in time and four in space based on half-step discretization for two-dimensional fourth order quasi-linear …
	2019

[3]	Stability and numerical approximation for a spacial class of semilinear parabolic equations on the Lipschitz bounded regions: Sivashinsky equation
	2019

[4]	Error analysis of a meshless weak form method based on radial point interpolation technique for Sivashinsky equation arising in the alloy solidification problem
	Journal of Computational and Applied Mathematics, 2018