A new numerical method for backward parabolic problems in the maximum-norm setting

摘要

A new method for solving numerically backward parabolic problems is proposed. As usual for this kind of ill posed problems, it is assumed that an a priori bound for the solution is available. The algorithm consists of two basic steps. First, a standard forward integration is performed, in order to approximate the solution at suitable future time levels. Second, a holomorphic recovery procedure is carried out, providing the required approximations for the preceding times. The analysis is valid in the maximum-norm setting, and rigorous estimates are derived. Among other advantages, the method can also be applied to nonlinear problems, and it produces a continuous output. Some numerical illustrations are presented. [References: 52]