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On the application of the method of fundamental solutions to nonlinear partial differential equations

Alves, Carlos J. S.; Silvestre, Ana Leonor

Engineering Analysis with Boundary Elements, 92 (2018), 267-274

This paper addresses the application of a domain-type method of fundamental solutions (MFS-D) together with a Picard iteration scheme for solving nonlinear elliptic partial differential equations. A mathematical justification of the iterative process and an {\em a posteriori} error estimate are provided for a class of nonlinear problems. Numerical simulations illustrate the convergence and accuracy of the method, in several examples, including a case for a sine-Gordon equation.