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Basic Concepts in Computational Physics pp 1–13Cite as

Some Basic Remarks

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Abstract

The need of numerical methods to solve problems in physics and related sciences is motivated by the classical problem of the harmonic oscillator beyond the small angle approximation. The calculation of the period of the harmonic oscillator immediately introduces the need of series expansions and as a consequence - the truncation error. Further possible numerical errors are recognized: floating point errors, errors due to subtractive cancellation, methodological errors, etc. Finally, the question of the stability of a numerical method and of its computational cost is raised.

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Notes

  1. 1.

    Although unstable behavior is not desirable in the first place the discovery of unstable systems was the birth of a specific branch in physics called Chaos Theory. We will come back to this point at the end of this section.

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Authors and Affiliations

  1. Faculty of Physics, University of Duisburg-Essen, Lotharstrasse 1-21, 47048, Duisburg, Germany

    Benjamin A. Stickler

  2. Institute of Theoretical and Computational Physics, Graz University of Technology, Graz, Austria

    Ewald Schachinger

Authors
  1. Benjamin A. Stickler
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  2. Ewald Schachinger
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Correspondence to Benjamin A. Stickler .

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© 2014 Springer International Publishing Switzerland

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Stickler, B.A., Schachinger, E. (2014). Some Basic Remarks. In: Basic Concepts in Computational Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-02435-6_1

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