This article is cited in 2 papers

Research on the convergence of an explicit difference scheme for a parabolic equation with a nonlinear nonlocal spatial operator

O. V. Glazyrina, M. F. Pavlova

Institute of Computer Mathematics and Information Technologies, Kazan (Volga Region) Federal University, Kazan, Russia

Abstract: We consider the first boundary value problem for a parabolic equation with a spatial operator degenerating with respect to the gradient. This operator also depends on the integral characteristic of the solution. We prove the convergence theorem for an explicit difference scheme under minimal assumptions on the smoothness of the initial data.

Keywords: parabolic equations, monotone operator, nonlocal operator, explicit difference scheme, stability, convergence.

UDC: 519.6

Received: 30.09.2013