Approximation with frequency filter for backward parabolic equations

Abstract

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. Classification (1991): 65M06, 65M12, 65M15 Mathematics Subject