The method of fundamental solutions belongs to meshless methods and was proposed in the early 1960s by V.D. Kupradze and M.A. Aleksidze. It was developed and successfully applied for many different problems. The basic advantages of this method are: ease of implementation, semi-analytical form of the approximate solution. In the method the approximate solution is a linear combination of fundamental solutions and coefficients of the solution are calculated using the boundary collocation technique.

In case of nonlinear problems the Picard iteration method is used and then the problem is converted into a sequence of inhomogeneous problems. Then on each iteration step the inhomogeneous problem is interpolated using the radial basis functions and simultaneously the particular solution is obtained. The general solution is obtained using the method of fundamental solution. This procedure will be demonstrated during the presentation.

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Anabela Oberheim
Sekretariat Prof. Dr. Schweitzer, Prof. Dr. Peterseim
Institut für Numerische Simulation
Rheinische Friedrich-Wilhelms Universität Bonn

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E-Mail: oberheim@ins.uni-bonn.de
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