The different computational methods for 2D parabolic boundary problems have been considered. It is assumed the coefficients of the equations are discontinuous and the lines of discontinuity don’t coincide with coordinate ones. It results in the necessity of using the non-orthogonal grids. The fully implicit, additive and regularized schemes have been developed. The specific method of regularization taking into account discontinuity of coefficient allows constructing the schemes more than first order of time approximation, which are easily parallelized.

Mathematical problems and theory of numerical methods