Computer Science – Numerical Analysis
Scientific paper
2004-12-31
APPLIED AND INDUSTRIAL MATHEMATICS IN ITALY, Series on Advances in Mathematics for Applied Sciences - Vol. 69, World Scientifi
Computer Science
Numerical Analysis
13 pages, 1 figure
Scientific paper
In this paper we present an estimate of accuracy for a piecewise polynomial approximation of a classical numerical solution to a non linear differential problem. We suppose the numerical solution U is computed using a grid with a small linear step and interval time Tu, while the polynomial approximation V is an interpolation of the values of a numerical solution on a less fine grid and interval time Tv << Tu. The estimate shows that the interpolant solution V can be, under suitable hypotheses, a good approximation and in general its computational cost is much lower of the cost of the fine numerical solution. We present two possible applications to linear case and periodic case.
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