Approximation with frequency filter for backward parabolic equations

We propose a numerical method for the initial (and boundary) value problem for the equation of the form \(u_t+Au=0\) where A is an unbounded, selfadjoint operator with negative spectrum. Roundoff errors in the numerical solution of such problem may generate a parasite term growing very quickly with time. To eliminate this parasite term, we apply a special finite difference equation with r free parameters. Similar ideas may be useful also for another numerically difficult differential problems.

Authors and Affiliations

1. Warsaw University, Department of Mathematics, Computer Science and Mechanics, Banacha 2, 02-097 Warszawa, Poland; e-mail: kmoszyns@appli.mimuw.edu.pl , , , , , , PL

   Krzysztof Moszyński

Received October 6, 1997 / revised version received November 26, 1998 / Published online October 16, 2000

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