Application of the Trefftz method to nonlinear potential problems - Uściłowska, Anita (Computer Assisted Methods in Engineering and Science; Vol 15 No 3-4 (2008), 2022)
In this paper some types of nonlinear potential problems are discussed and some of these problems are solved by the Trefftz method. The attention is paid to Fundamental Solutions Method (FSM) supported by Radial Basis Functions (RBF) approximation. Application of FSM to nonlinear boundary problem requires certain modifications and special algorithms. In this paper two methods of treating the nonlinearity are proposed. One on them is Picard iteration. Due to some problems of application of this method the Homotopy Analysis Method (HAM) is implemented for nonlinear boundary-value problems. The results of numerical experiment are presented and discussed. The conclusion is that the method based on FSM for solving nonlinear boundary-value problem gives result with demanded accuracy.