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.
The roots of a real valued polynomial of order N = 3 or 4 are referred to as Cardano’s or Ferrari’s solutions [13], respectively.
- 2.
A disastrous effect of this binary approximation of 0.1 was discussed by T. Chartier [14].
- 3.
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 briefly comment on this point at the end of this section.
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Stickler, B.A., Schachinger, E. (2016). Some Basic Remarks. In: Basic Concepts in Computational Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-27265-8_1
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