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

• 作者: Marco Schuchmann Michael Rasguljajew
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: ODE Sinc COLLOCATION Shannon WAVELET WAVELET COLLOCATION ERROR ESTIMATION
• 年，卷（期）: 2013,（2）
• 页码范围: 114-120
• 页数: 7页
• 分类号: O1

摘要

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.