A conservative differencing sceme for diffusion-type equations on base of multigrid methods

The new effective solution algorithm for parabolic equations on base of multigrid method is offered, which has stability, accuracy and conservation laws inherent in the implicit scheme and allows to reduce essentially the volume of arithmetical work on each time level. The absolute stability, conservation laws and convergence of proposed method are theoretical proved for model initial-boundary problems for one-dimensional and two-dimensional heat conduction equations, the accuracy estimations are obtained. Calculations of two-dimensional modeling problems including with explosive factors have shown a good accuracy of offered method.