BIT Numerical Mathematics

, Volume 47, Issue 3, pp 487–505 | Cite as

Approximations of parabolic integro-differential equations using wavelet-Galerkin compression techniques

Article

Abstract

Error estimates for Galerkin discretizations of parabolic integro-differential equations are presented under minimal regularity assumptions. The analysis is applicable in case that the full Galerkin matrix A associated to the integral operator is replaced by a compressed “sparse” matrix \(\mathbf{\tilde{A}}\) using wavelet basis techniques. In particular, a semi-discrete (in space) scheme and a fully-discrete scheme which is discontinuous in time but conforming in space are analyzed.

Key words

parabolic integro-differential equations error estimates wavelet compression techniques discontinuous Galerkin method minimal regularity 

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Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of MathematicsNational Technical University, Zografou CampusAthensGreece

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