TITLE:
Error Estimation and Assessment of an Approximation in a Wavelet Collocation Method
AUTHORS:
Marco Schuchmann, Michael Rasguljajew
KEYWORDS:
ODE; Sinc Collocation; Shannon Wavelet; Wavelet Collocation; Error Estimation
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.3 No.2,
June
24,
2013
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.