Bernal Martínez, Francisco Manuel2021-03-112021-03-112016-10Bernal, F. (2016). Trust-region methods for nonlinear elliptic equations with radial basis functions. Computers & Mathematics with Applications, 72(7), 1743–1763.0898-1221https://hdl.handle.net/10016/32113We consider the numerical solution of nonlinear elliptic boundary value problems with Kansa's method. We derive analytic formulas for the Jacobian and Hessian of the resulting nonlinear collocation system and exploit them within the framework of the trust-region algorithm. This ansatz is tested on semilinear, quasilinear and fully nonlinear elliptic PDEs (including Plateau's problem, Hele-Shaw flow and the Monge-Ampère equation) with excellent results. The new approach distinctly outperforms previous ones based on linearization or finite-difference Jacobians.21eng© 2016 Elsevier Ltd.Atribución-NoComercial-SinDerivadas 3.0 EspañaKansa's methodRadial basis functionNonlinear elliptic PDETrust-region methodMonge-AmpèrePlateau's problemresearch articleMatemáticashttps://doi.org/10.1016/j.camwa.2016.07.014open access174371763Computers & Mathematics with Applications72AR/0000026520