## Abstract

An implicit numerical method is introduced that gives piecewise polynomial spline approximations for the solution of an initial value problem for the equation

\(y'(t)=f(t,y(t)).\)

Here, \(f\) is a function having continuous derivatives up to the order \(r\). The method presented in this work, provides spline functions which approximate the solution of the problem in the most regular function space \(C^{r+1}\). Error estimates in \(C\) and \(C^{r+1}\) are given and the stability of the method is investigated.

## Authors

**Gh. Micula
**Babes-Bolyai University of Cluj-Napoca, Faculty of Mathematics, Cluj-Napoca, Romania

**A. Revnic**

Romanian Academy, Popoviciu Institute of Numerical Analysis, Cluj-Napoca , Romania

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## Paper coordinates

G. Micula, A. Revnic, *An implicit numerical spline method for systems for ODEs**,* Appl. Math. Comp., 111 (2000) 121-132

doi: 10.1016/S0096-3003(98)10111-X

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