Numerical computations and mathematical modelling with infinite and infinitesimal numbers

Journal of Applied Mathematics and Computing 29:177-195 (2009)
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Abstract

Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not related to the non-standard analysis) is used to work with finite, infinite, and infinitesimal numbers numerically. This can be done on a new kind of a computer – the Infinity Computer – able to work with all these types of numbers. The new computational tools both give possibilities to execute computations of a new type and open new horizons for creating new mathematical models where a computational usage of infinite and/or infinitesimal numbers can be useful. A number of numerical examples showing the potential of the new approach and dealing with divergent series, limits, probability theory, linear algebra, and calculation of volumes of objects consisting of parts of different dimensions are given.

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Yaroslav Sergeyev
Università della Calabria

References found in this work

Non-standard Analysis.Gert Heinz Müller - 1966 - Princeton University Press.
Contributions to the Founding of the Theory of Transfinite Numbers.Cassius J. Keyser - 1916 - Journal of Philosophy, Psychology and Scientific Methods 13 (25):697-697.

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