Cauchy Problem For The Biharmonic EquationSolved Using The Regularization Method

The boundary element method (BEM) is applied to discretise numerically a Cauchy problem for the biharmonic equation which involves over- and underspecified boundary portions of the solution domain. The resulting ill-conditioned system of linear equations is solved using the regularization method. It is shown that the regularization method performs better than the minimal energy method in the case of the biharmonic equation, unlike the Laplace equation where the minimal energy method is more efficient. Moreover, the stability of the numerical solution obtained by the regularization method is also investigated.