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

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 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.