Mixed Boundary Value Problems for some Linear and Non-linear Elliptic Difference Equations

1 April 1972

journal article
Published by Oxford University Press (OUP) in IMA Journal of Applied Mathematics

Vol. 9 (2) , 205-217
https://doi.org/10.1093/imamat/9.2.205

Abstract

We obtain a priori bounds on difference quotients for some mixed boundary value problems associated with uniformly elliptic difference equations over rectangular regions. These results are applied to mildly quasi-linear and mildly non-linear problems to establish existence and uniqueness criteria. Our estimates are useful in the numerical computation of these solutions.

Keywords

DIFFERENCE EQUATIONS
BOUNDARY VALUE PROBLEMS
ELLIPTIC DIFFERENCE
LINEAR ELLIPTIC
MIXED BOUNDARY VALUE

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