A Stable Difference Scheme for the Mixed Boundary Problem for a Hyperbolic, First-Order System in Two Dimensions

1962 ◽  
Vol 10 (2) ◽  
pp. 229-245 ◽  
Author(s):  
Vidar Thomée
Keyword(s):  
Difference Scheme ◽  
Boundary Problem ◽  
Mixed Boundary ◽  
Two Dimensions ◽  
Order System ◽  
First Order ◽  
Mixed Boundary Problem

Finite-difference techniques for a harmonic mixed boundary problem having a reentrant boundary

1971 ◽  
Vol 323 (1553) ◽  
pp. 271-276 ◽  
Keyword(s):  
Exact Solution ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Uniform Convergence ◽  
Boundary Problem ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Mixed Boundary Value Problem ◽  
Mixed Boundary Problem ◽  
Finite Difference Techniques

The proof of uniform convergence of a family of finite-difference solutions to the exact solution is outlined for a harmonic mixed boundary-value problem in a rectangle containing a slit. Finite-difference results in the neighbourhood of the tip of the slit are given for reference.

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