Affiliation:
1. Nuclear Safety Institute , Russian Academy of Sciences, 52, B. Tulskaya, 115191; and Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198 Moscow , Russia
Abstract
Abstract
In numerical solving boundary value problems for parabolic equations,
two- or three-level implicit schemes are in common use. Their computational implementation is based on
solving a discrete elliptic problem at a new time level.
For this purpose, various iterative methods are applied to multidimensional problems
evaluating an approximate solution with some error.
It is necessary to ensure that these errors do not violate the stability of the
approximate solution, i.e., the approximate solution must converge to the exact one.
In the present paper, these questions are investigated in numerical solving a Cauchy problem for a linear evolutionary equation of first order, which is considered in a finite-dimensional Hilbert space.
The study is based on the general theory of stability (well-posedness) of operator-difference schemes developed by Samarskii.
The iterative methods used in the study are considered from the same general positions.
Funder
Ministry of Education and Science of the Russian Federation
Subject
Applied Mathematics,Computational Mathematics,Numerical Analysis
Reference22 articles.
1. U. M. Ascher,
Numerical Methods for Evolutionary Differential Equations,
Comput. Sci. Eng. 5,
Society for Industrial and Applied Mathematics, Philadelphia, 2008.
2. J. H. Bramble, J. E. Pasciak, P. H. Sammon and V. Thomée,
Incomplete iterations in multistep backward difference methods for parabolic problems with smooth and nonsmooth data,
Math. Comp. 52 (1989), no. 186, 339–367.
3. J. H. Bramble and P. H. Sammon,
Efficient higher order single step methods for parabolic problems. I,
Math. Comp. 35 (1980), no. 151, 655–677.
4. S. C. Brenner and L. R. Scott,
The Mathematical Theory of Finite Element Methods, 3rd ed.,
Springer, New York, 2008.
5. T. A. Davis,
Direct Methods for Sparse Linear Systems,
Fundam. Algorithms 2,
Society for Industrial and Applied Mathematics, Philadelphia, 2006.
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献