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Introduction to Adaptive Methods for Differential Equations

Published online by Cambridge University Press:  07 November 2008

Kenneth Eriksson ,
Don Estep ,
Peter Hansbo  and
Claes Johnson
Kenneth Eriksson
Affiliation:
Mathematics Department, Chalmers University of Technology, 412 96 Göteborgkenneth@math.chalmers.se
Don Estep
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta GA 30332estep@pmath.gatech. edu
Peter Hansbo
Affiliation:
Mathematics Department, Chalmers University of Technology, 412 96 Göteborghansbo@math.chalmers.se
Claes Johnson
Affiliation:
Mathematics Department, Chalmers University of Technology, 412 96 Göteborgclaes@math.chalmers.se
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Abstract

Knowing thus the Algorithm of this calculus, which I call Differential Calculus, all differential equations can be solved by a common method (Gottfried Wilhelm von Leibniz, 1646–1719).

When, several years ago, I saw for the first time an instrument which, when carried, automatically records the number of steps taken by a pedestrian, it occurred to me at once that the entire arithmetic could be subjected to a similar kind of machinery so that not only addition and subtraction, but also multiplication and division, could be accomplished by a suitably arranged machine easily, promptly and with sure results…. For it is unworthy of excellent men to lose hours like slaves in the labour of calculations, which could safely be left to anyone else if the machine was used…. And now that we may give final praise to the machine, we may say that it will be desirable to all who are engaged in computations which, as is well known, are the managers of financial affairs, the administrators of others estates, merchants, surveyors, navigators, astronomers, and those connected with any of the crafts that use mathematics (Leibniz).

Type
Research Article
Information
Acta Numerica , Volume 4 , January 1995 , pp. 105 - 158
Copyright
Copyright © Cambridge University Press 1995

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References

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