On error of certain projection-grid methods for an ordinary differential equation of 4-th order with non-smooth data
type: Item
instance of: scholarly article
title: On error of certain projection-grid methods for an ordinary differential equation of 4-th order with non-smooth data
zbMATH Open document ID: 0843.65059
author: O. I. Kireeva
author: Alexander Zlotnik
published in: Russian Mathematics
publication date: 1996-05-12T00:00:00Z
review text: The boundary value problem for the differential equation \((a_2 u'')''- (a_1 u')'+ a_0 u= f\), \(x\in \Omega= (0, X)\), \(u(0)= u'(0)= u(X)= u'(X)= 0\) is studied. The coefficients are measurable and bounded, \(f\in L_p(\Omega)\) or \(f\) is a generalized function. A projective grid method, which uses generalized piecewise ``cubic'' Hermitian splines, is studied. Bounds of the error in the norm of \(W^2_2(\Omega)\) in dependence of properties of \(a_1\), \(a_2\) and \(f\) are obtained.
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 65L10
zbMATH DE Number: 857503
zbMATH Keywords: fourth-order equation
zbMATH Keywords: error estimations
zbMATH Keywords: cubic Hermitian splines
zbMATH Keywords: projective grid method
reviewed by: Miroslav Bartušek
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 857503