Numerical solution of parabolic equations on locally-adaptive grids by Chebyshev method

Some aspects of the solution of parabolic equations on Cartesian locally adaptive grids are considered. We represent main features of the algorithm and describe some results of experimental study of accuracy the presented computational technique. For time integration it is used the explicit Chebyshev iterative scheme LI-M. The results of numerical experiments are given for model problems including case of continuous and discontinuous coefficients. We demonstrate performance of the grid operator library, which ensures the transfer of the program on graphics accelerators CUDA and does not require from a user deep knowledge of programming techniques for CUDA.