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

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 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. AMS subject classification (2000)  65R20, 65M60