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Infinitely differentiable functions represented into Newton interpolating series. (English) Zbl 1349.41051

Summary: We study infinitely differentiable functions which are representable into a Newton interpolating series at a suitable interpolation sequence with terms in \([0,1]\). Applications of this series to approximate the solution of boundary value problems for linear systems of differential equations are presented.

MSC:

41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations
65L10 Numerical solution of boundary value problems involving ordinary differential equations
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