A New Kind of Schemes for the Operator Equations

Abstract

This paper provides a new kind of three-layer explicit schemes for solving the operator equation. It has good stability, and suits particularly the semidiscrete problems arising from solving multi-dimensional parabolic-type equations by the finite element method. The amount of its computation time is far less than that of various economical schemes of the difference method. If the accuracy of the nonstandard finite element schemes (2.7) is not enough, it can be improved using extrapolations.