A note on the second order of accuracy difference scheme for elliptic-parabolic equations in Hölder spaces

Abstract

The present paper is devoted to the study of a second order of accuracy difference scheme for a solution of the elliptic-parabolic equation with nonlocal boundary condition. The well-posedness of the second order of accuracy difference scheme in H¨older spaces is established. Coercivity estimates in H¨older norms for an approximate solution of a nonlocal boundary value problem for elliptic-parabolic differential equation are obtained. Results of numerical experiments are presented in order to support the aforementioned theoretical statements.