A fast computing technique for diffusion-type equations (Q1078990)

A numerical method is presented which decreases the computing time, needed to solve diffusion-type equations, considerably (a factor 3 is mentioned) if compared to classical methods. The main idea of the method is to cancel all ''odd''-point equations in the resulting discretized system and expressing the ''odd''-unknowns, which would still be present in the ''even'' equations, either in ''even''-unknowns using analytical relations or in ''odd''-unknowns using earlier time-steps. The whole procedure is related to the well-known odd-even Hopscotch method. However no reference to this method is made. Moreover it is claimed that the accuracy is not affected while the stability is improved. However, the improvement of the stability is a result of the extra diffusion introduced by the ''odd-even'' technique, hence the accuracy should be affected accordingly.