I’m interested in solving nonlinear elliptic boundary value problems of the type $$ -a\Delta u + f(u) = 0, $$ $$ u|_\Gamma = u_0 $$ by Newton’s method when its convergence is global and monotonic. Could you advice some references concerning this problem, containing proofs of global convergence?

Newton's method takes the form $$ -a\Delta u + f(\widetilde u) + f'(\widetilde u)(u - \widetilde u) = 0 $$ where $\widetilde u$ is the previous approximation for the solution.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.