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The purpose of this study is to propose a high-accuracy and fast numericalmethod for the Cauchy problem of the Laplace equation. Our problem is directlydiscretized by the method of fundamental solutions (MFS). The Tikhonovregularization method stabilizes a numerical solution of the problem for givenCauchy data with high noises. The accuracy of the numerical solution depends ona regularization parameter of the Tikhonov regularization technique and someparameters of MFS. The L-curve determines a suitable regularization parameterfor obtaining an accurate solution. Numerical experiments show that such asuitable regularization parameter coincides with the optimal one. Moreover, abetter choice of the parameters of MFS is numerically observed. It isnoteworthy that a problem whose solution has singular points can successfullybe solved. It is concluded that the numerical method proposed in this paper iseffective for a problem with an irregular domain, singular points, and theCauchy data with high noises.

Method of Fundamental Solutions with Optimal Regularization Techniques for the Cauchy Problem of the Laplace Equation with Singular Points