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).


65D15 Algorithms for approximation of functions
65L05 Numerical methods for initial value problems involving ordinary differential equations
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