Abstract. Least squares collocation method (LSC) is a versatile numerical method for solving boundary value problems for PDE. The present article demonstrates the abilities of LSC to solve various problems -in particular, calculations of bending of isotropic irregular shaped plates and multi-layered anisotropic plates. In order to achieve higher accuracy, new versions of the method utilize high-degree polynomial spaces. The numerical experiments demonstrate high accuracy of the solutions.
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.
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