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S. Bertoluzza, “Adaptive Wavelet Collocation Method for the Solution of Burgers Equation,” Transport Theory and Statistical Physics, Vol. 25, No. 3-5, 2006, pp. 339-352. doi:10.1080/00411459608220705

has been cited by the following article:

• 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.