ISSN:
0945-3245
Keywords:
(AMS) 65L10
;
CR 5.17
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary Let (m!)−1 D m y H denote them-th divided difference of a grid functiony H . For the numerical solution of boundary value problems of ordern we consider compact discretizations on nonuniform grids. We prove the stability inequality $$\sum\limits_{i = 0}^{n - 1} {||D_i y_H } ||_{H, \infty } \leqq c\left\{ {||L_H y_H ||_{H.1} + \sum\limits_{l = 0}^{n - 1} {|B_{H, l} (y_H )|} } \right\}$$ whereL H andB H, l are the discretizations of the differential operatorL and the boundary conditionsB l respectively and ∥·∥ H.1 denotes a discreteL 1-norm, provided the discretization is consistent. Furthermore, no condition upon the grid is needed.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01399012
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