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Implementation of the Recursive Formula for Evaluation of the Strength of Daniels’ Model

Authors: Václav Sadílek, Miroslav Vořechovský


The paper deals with the classical fiber bundle model of equal load sharing, sometimes referred to as the Daniels’ bundle or the democratic bundle. Daniels formulated a multidimensional integral and also a recursive formula for evaluation of the strength cumulative distribution function. This paper describes three algorithms for evaluation of the recursive formula and also their implementations with source codes in the Python high-level programming language. A comparison of the algorithms are provided with respect to execution time. Analysis of orders of magnitudes of addends in the recursion is also provided.

Keywords: Python, equal load sharing, mpmath, Daniels bundle model

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