×

Increase of accuracy in solving differential equations with singularities of the type 0/0 by a right choice of an additional term. (English) Zbl 0545.65009

Indefinite expressions of the type \(z(t)=f(t)/g(t),\) where \(\lim_{t\to 0}f(t)=\lim_{t\to 0}g(t)=0\), are modelled in the form \[ z(t)\doteq(f(t)+az(0) \exp(-\alpha t))/(g(t)+a \exp(-\alpha t)), \] where \(z(0)= \lim_{t\to 0}f(t)/g(t)\). Optimal values of the coefficients a and \(\alpha\) are determined for some cases of f(t) and g(t).

MSC:

65D15 Algorithms for approximation of functions
65L05 Numerical methods for initial value problems involving ordinary differential equations
PDFBibTeX XMLCite
Full Text: EuDML

References:

[1] Beneš K.: Vznik nespojitostí výstupního napětí při modelování podílu pomocí diodové násobičky. Elektrotechn. časopis 20, 1961, č. 1, str. 45-59.
[2] Beneš K.: Zvýšení přesnosti při modelování podílu dvou funkcí. Elektrotechn. časopis 28, 1977, č. 7, str. 481-493.
[3] Borský J., Matyáš J.: Technika použití elektronických analogových počítačů. SNTL Praha 1963.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.