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.
A mathematical model of nonlinear deformation of ice samples from distilled water is implemented. An algorithm for numerical solution of corresponding boundary-value problem is proposed and realized. Results of the numerical modeling have been compared to experimental data on the three-point bending of ice beams.
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