Open AccessThe least squares collocation method for the biharmonic equation in irregular and multiply-connected domains
Author(s) -
В. П. Шапеев,
Sergey Golushko,
Luka Bryndin,
Vasily Belyaev
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1268/1/012076
Subject(s) - biharmonic equation , collocation (remote sensing) , mathematics , least squares function approximation , boundary value problem , mathematical analysis , collocation method , computer science , differential equation , ordinary differential equation , statistics , machine learning , estimator
This paper reports new h-and p-versions of the least squares collocation method of high-order accuracy proposed and implemented for solving boundary value problems for the biharmonic equation in irregular and multiply-connected domains. This paper shows that approximate solutions obtained by the least squares collocation method converge with high order and agree with analytical solutions of test problems with high degree of accuracy. There has been a comparison made for the results achieved in this study and results of other authors who used finite difference and spectral methods.