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An estimate of accuracy for interpolant numerical solutions of a PDE problem

2004/12/31 by Gianluca Argentini, Argentini, Gianluca
Mathematics · #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #G.1.8 #Mathematical Physics (math-ph) #Numerical Analysis (math.NA) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.cs/0412120

openalex publication_date 2004/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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