SOME INSIGHTS INTO THE STABILITY OF DIFFERENCE APPROXIMATIONS FOR HYPERBOLIC INITIAL-BOUNDARY-VALUE PROBLEMS

1986 ◽  
pp. 171-176 ◽  
Author(s):  
Robert F. Warming ◽  
Richard M. Beam
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Difference Approximations ◽  
The Stability ◽  
Initial Boundary Value

Difference approximations for initial boundary-value problems

1971 ◽  
Vol 323 (1553) ◽  
pp. 255-261 ◽  
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Difference Approximations ◽  
Strengthened Form ◽  
The Stability ◽  
Initial Boundary Value ◽  
Scalar Equations

The problem of the stability of difference approximations for initial boundary-value problems is examined and recent results obtained in this field by Gustafsson, Kreiss & Sundström (1971) are presented. It is shown that even for scalar equations the Ryabenkii-Godunow condition is not sufficient for stability and a procedure is outlined which leads to a slightly strengthened form of this condition which is satisfactory in practice.

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