Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Stability of difference approximations of dissipative type for mixed initial-boundary value problems. I

Author: Stanley Osher
Journal: Math. Comp. 23 (1969), 335-340
MSC: Primary 65.67
MathSciNet review: 0246530
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: H. O. Kreiss, [2], has recently extended the stability theory of difference approximations to include the hyperbolic system

$\displaystyle u_t = A{u_x},0 \leqq x,t$

, with $ A$ a diagonal matrix. Appropriate boundary and initial conditions are given. The amplification matrix $ \hat Q(\xi )$ need not be diagonal. However, he required that $ \vert\hat Q(\xi )\vert \leqq 1$. We use certain results in matrix theory and Wiener-Hopf factorization to replace this restrictive assumption by certain reasonable assumptions on accuracy of $ \hat Q(\xi )$ and smoothness of an associated positive-definite symmetric matrix. This technique will be important in half-space problems in many space variables since for such problems the amplification matrix will certainly not be diagonal.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65.67

Retrieve articles in all journals with MSC: 65.67

Additional Information

Article copyright: © Copyright 1969 American Mathematical Society

American Mathematical Society