# An implicit numerical spline method for systems for ODEs

## 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

## Keywords

Deficient spline function; Implicit method; Stability condition; Stiff systems; Region of stability

### References

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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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## About this paper

##### Journal

Applied Mathematics and Computation

Elsevier

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