Journal of Numerical Mathematics
Editor-in-Chief: Hoppe, Ronald H. W. / Kuznetsov, Yuri
Managing Editor: Olshanskii, Maxim
Editorial Board: Benzi, Michele / Brenner, Susanne C. / Carstensen, Carsten / Dryja, M. / Feistauer, Miloslav / Glowinski, R. / Lazarov, Raytcho / Nataf, Frédéric / Neittaanmaki, P. / Bonito, Andrea / Quarteroni, Alfio / Guzman, Johnny / Rannacher, Rolf / Repin, Sergey I. / Shi, Zhong-ci / Tyrtyshnikov, Eugene E. / Zou, Jun / Simoncini, Valeria / Reusken, Arnold
4 Issues per year
IMPACT FACTOR 2017: 0.951
5-year IMPACT FACTOR: 3.128
CiteScore 2017: 0.96
SCImago Journal Rank (SJR) 2017: 0.494
Source Normalized Impact per Paper (SNIP) 2017: 0.772
Mathematical Citation Quotient (MCQ) 2016: 1.02
Uniformly convergent numerical method for solving modified Burgers' equations on a non-uniform mesh
In this paper, we consider the one-dimensional modified Burgers' equation in the finite domain. This type of problem arises in the field of sonic boom and explosions theory. At the high Reynolds' number there is a boundary layer in the right side of the domain. From the numerical point of view, one of the difficulties in dealing with this problem is that even smooth initial data can give rise to solution varying regions, i.e., boundary layer regions. To tackle this situation, we propose a numerical method on non-uniform mesh of Shishkin type, which works well at high as well as low Reynolds number. The proposed numerical method comprises of Euler implicit and upwind finite difference scheme. First we discretize in the temporal direction by means of Euler implicit method which yields the set of ordinary differential equations at each time level. The resulting set of differential equations are approximated by upwind scheme on Shishkin mesh. The proposed method has been shown to be parameter uniform and of almost first order accurate in the space and time. An extensive amount of analysis has been carried out in order to prove parameter uniform convergence of the method. some test examples have been solved to verify the theoretical results.
Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.