On patterns of the method of lines of high accuracy for some two-dimensional parabolic equations

An application of the method of lines to the first mixed problem for two-dimensional half-linear and linear parabolic equations denned in a cylindrical domain with a rectangular foundation is considered. For the half-linear equation the scheme of an accuracy $O(h^3)$ is constructed. For the linear equation with the coefficients being functions only of time $t$ the scheme of any accuracy for corresponding accuracy of approximation is constructed. Bibliography: 7 titles.