Approximation with frequency filter for backward parabolic equations

Summary. 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.