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On the method of backward steps of Carathéodory-Tonelli. (English) Zbl 0857.34027

Solving the Cauchy problem for ordinary differential equations by using the Carathéodory-Tonelli method of backward steps a sequence of functions is inductively constructed. This paper is devoted to the study of convergence of this sequence.

MSC:

34A45 Theoretical approximation of solutions to ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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