Differential approximation as a qualitative test for difference schemes

1981 ◽  
Vol 21 (5) ◽  
pp. 581-587
Author(s):  
A. I. Urusov ◽  
Yu. I. Shokin ◽  
N. N. Yanenko
Keyword(s):  
Difference Schemes ◽  
Differential Approximation ◽  
Qualitative Test

Symmetrizable Difference Dchemes

2005 ◽  
Vol 5 (1) ◽  
pp. 3-50 ◽  
Author(s):  
Alexei A. Gulin
Keyword(s):  
Initial Data ◽  
Difference Scheme ◽  
Difference Schemes ◽  
Time Dependent ◽  
Stability Boundaries ◽  
Typical Representative ◽  
Variable Weight ◽  
The Stability ◽  
Conditions Of Stability ◽  
The Right

AbstractA review of the stability theory of symmetrizable time-dependent difference schemes is represented. The notion of the operator-difference scheme is introduced and general ideas about stability in the sense of the initial data and in the sense of the right hand side are formulated. Further, the so-called symmetrizable difference schemes are considered in detail for which we manage to formulate the unimprovable necessary and su±cient conditions of stability in the sense of the initial data. The schemes with variable weight multipliers are a typical representative of symmetrizable difference schemes. For such schemes a numerical algorithm is proposed and realized for constructing stability boundaries.

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