Homogeneous difference schemes on non-uniform nets for equations of parabolic type

Abstract

The basic problems of the theory of homogeneous difference schemes for linear, quasi-linear aud non-linear equations of parabolic type have been studied in a number of works ([ll151). The stability, convergence, and also estimates of the rate of convergence (order of accuracy) of several families of homogeneous difference schemes in the classes of continuous aud ~s~tinu~ coefficients of the differential equation have been established. In [sl attention was paid to the fact that on an arbitrary sequence of non-uniform nets difference schemes which have second order approximation on uniform nets have only first order approximation. For this reason the problem of the order of accuracy on non-uuiform nets requires special study. A family of homogeneous difference schemes on non-uniform nets for the equation