APPLICATION OF MULTIGRID TECHNIQUES FOR SOLVING PARABOLIC EQUATIONS
M. E. Ladonkina, O. Yu. Milyukova, V. F. Tishkin
VANT. Ser.: Mat. Mod. Fiz. Proc 2008. Вып.1. С. 4-19.
New effective solution algorithm for parabolic equations based on multigrid technique is suggested which maintains virtues of implicit scheme — stability and accuracy. At the same time this algorithm allows to considerably reduce number of arithmetical operations on each time layer. Absolute stability of the suggested technique is theoretically proved by example of one-dimensional model problem. Accuracy of the technique is investigated by example of two-dimensional model problem. It is proved that for model problem solution obtained using the suggested technique differs little from solution for implicit scheme on explicit grid. Computations of one- and two-dimensional problems with continuous and discontinuous coefficients show good accuracy of the suggested technique.
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English
