Journal Article10.1016/0362-546X(83)90056-1
On computing Darboux type series analyses
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TL;DR: In this paper, the reliability of the estimates for the location and the order of primary singularities is estimated by comparing two sets of estimates at the same stage instead of by comparing estimates from different stages.
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Abstract: 1 The reliability of the estimates for the location and the order of primary singularities is estimated by comparing two sets of estimates at the same stage instead of by comparing estimates from different stages 2 The system of nonlinear equations which must be solved for the location and order of the primary singularities at each stage is replaced by a linear system which is much easier to solve
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References
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C. Hunter,B. Guerrieri +1 more
TL;DR: In this paper, the authors present two iterative algorithms for determining the parameters of the closest singularity in the Taylor series expansion of an analytic function about some point, which are based on the consequent asymptotic formulas for the coefficients as given by Darboux's theorem.
Transformation methods in the analysis of series for critical properties
TL;DR: In this article, the authors discuss the theory of transformations and provide a rational and systematic method of approach to the problem of choosing the most suitable transformation for a given series, and show that, for series likely to arise in thermodynamics, it is always possible to find transformations which achieve this purpose.
Solving Ordinary Differential Equations Using Taylor Series
George F. Corliss,Y. F. Chang +1 more
TL;DR: The included Taylor series method executes faster and yields a more accurate answer than the standard methods for most of the problems in the test set and is most attractwe for small systems and for stringent accuracy tolerances.