On high accuracy schemes of the method of straight lines for two-dimensional parabolic equations

The method of straight lines is applied to the first mixed problem for two-dimensional semilinear and linear parabolic equations defined in a domain with rectangular base. For a semilinear equation, a scheme of accuracy O(h³) is obtained. For a linear equation with coefficients that are functions only of t, a scheme of any given accuracy is obtained under the relevant accuracy of the approximation. Bibliography:7 titles. Translated fromZapiski Nauchnykh Seminarov POMI, VOl. 219, 1994, pp. 81–93. This paper was supported by the International Foundation of Cultural Initiative and by the Russian Academy of Natural Sciences. Translated by N. S. Zabavnikova.