A new numerical method for the solution of parabolic equations on triangular grids based on the use of multigrid techniques is proposed. Numerical results obtained for model initial-boundary problems for heat conduction equation have demonstrated good accuracy of the method. The use of the proposed method for the solution of the heat conduction equation make it possible to reduce considerably the computational costs as compared either to the solution with the use of the fully implicit scheme on the fine grid or to the solution using the explicit scheme with a small time step-size.

parabolic type equations, multigrid methods, accuracy of numerical methods

Mathematical problems and theory of numerical methods