In this paper, the convergence of discrete flux in the difference scheme for the linear parabolic equation with discontinuous coefficients is disucssed. It is shown that the discrete flux of the difference scheme tends to the continuous flux of the differential equation in the sense of the maximum norm and the rate of convergence is O( r+ h1/2).
In this paper, the convergence of segment explicit-implicit difference scheme forthe parabolic equation with discontinuous coefficients is discussed. The truncationerror of the difference scheme neighboring the points of discontinuity of the coefficients is O(1). It is shown that the solution of the difference scheme tends to thesolution of the differential equation in the sense of the maximum norm and therate of convergence is O(τ + ). Moreover, the numerical flux of the differencescheme tends to the flux of the differential equation in the mean, while the rate ofconvergence is O(τ + h).
