Error Estimation and Assessment of an Approximation in a Wavelet Collocation Method

Marco Schuchmann, Michael Rasguljajew

University of Applied Science, Darmstadt, Germany.

DOI: 10.4236/ajcm.2013.32019                

Abstract

This article describes how to assess an approximation in a wavelet collocation method which minimizes the sum of squares of residuals. In a research project several different types of differential equations were approximated with this method. A lot of parameters must be adjusted in the discussed method here. For example one parameter is the number of collocation points. In this article we show how we can detect whether this parameter is too small and how we can assess the error sum of squares of an approximation. In an example we see a correlation between the error sum of squares and a criterion to assess the approximation.

Keywords

ODE; Sinc Collocation; Shannon Wavelet; Wavelet Collocation; Error Estimation

Conflicts of Interest

The authors declare no conflicts of interest.

References

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