Algorithmic progress in solving partial differential equations

ABSTRACT

This is an attempt to document the progress that has been made over the past 30 years in computational methods for solving partial differential equations. Hopefully the assumptions made in this study are clear, but they may well be disputed. Some computational efforts are quickly estimated here, but others are taken from the literature without an independent check that the same definition of effort is used. There are probably some computational methods which I have overlooked which should be included. Note that this study shows up some obscure methods as being very attractive, which suggests that there are other lesser known methods which are also attractive.

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