Trust-region methods for nonlinear elliptic equations with radial basis functions

Francisco Bernal

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


We 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.
Original languageEnglish (US)
Pages (from-to)1743-1763
Number of pages21
JournalComputers and Mathematics with Applications
Issue number7
StatePublished - Sep 19 2016
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2022-06-08
Acknowledgements: Portuguese FCT funding under grant SFRH/BPD/79986/2011 and a KAUST Visiting Scholarship at OCCAM in the University of Oxford are acknowledged.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics


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