Modified method of fundamental solutions for the Cauchy problem connected with the Laplace equation.

In this paper, a numerical algorithm is proposed based on the method of fundamental solutions (MFS) for the Cauchy problem connected with the Laplace equation in ℝ2. The major advantage of the modified MFS is to keep a very basic natural property, i.e. the invariance under trivial coordinate changes in the problem description. The method combines Newton's method and classic Tikhonov regularization to solve an inverse problem. The numerical convergence, accuracy, and stability of the method with respect to increasing the number of source points, and decreasing the amount of noise added into the input data, respectively, are also analysed with some examples, even for high noise levels. [ABSTRACT FROM PUBLISHER]