A Numerical Method for Constructing Attractors of Evolutionary Filtration Equations

Abstract

A numerical method is proposed to construct attractors of evolution equations describing the process of filtration of a two-phase liquid with allowance for capillary forces (the Rapoport-Leas model). The stability conditions for the proposed method are the conditions under which the third-order dynamics is an attractor for the initial equation. The solution of the initial equation is an iterative process, which can be paralleled to accelerate calculations.