The error estimation and its justification by the filtration of numerical results obtained with different numbers of nodes

In the paper the obtained results error is estimated by the filtration of numerical data computed with different nodes numbers. In order to check the existence of possibility of programming errors and other additional errors the comparison of uncertainty intervals defined by different numerical methods is applied. The solution of the problem of Stokes's solitary wave is considered as an example. The boundary conditions are given in a differential form in this work. The solving of the problem by new method with greater accuracy allows establishing the fact of incorrectness of some estimates received earlier by the other authors and also say about reliability of the estimates received by the filtration methods.