Abstract
We apply the class of Chen-Mangasarian smooth approximation functions and the smoothing Newton method proposed in [6] to solve a class of quasi-linear nonsmooth Dirichlet problems. We show that the smoothing Newton method converges globally and superlinearly for solving the system of nonsmooth equations arising from nonsmooth Dirichlet problems. Moreover, we show that the error bound for finite difference solution of smooth Poisson-type equations in a bounded domain [15] remains the same order for a class of nonsmooth equations. It is thus expected that the smoothing Newton method works well for nonsmooth Dirichlet problems. We report encouraging numerical results for three examples arising from a model of the ideal MHD equilibria.Key Wordsnonsmooth Dirichlet problemerror boundsmoothing Newton methods.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.