Karatson, Janos2019-12-182019-12-182000-06-30Karatson, J. (2000). Gradient method in Sobolev spaces for nonlocal boundary-value problems. <i>Electronic Journal of Differential Equations, 2000</i>(51), pp. 1-17.1072-6691https://hdl.handle.net/10877/9114An infinite-dimensional gradient method is proposed for the numerical solution of nonlocal quasilinear boundary-value problems. The iteration is executed for the boundary-value problem itself (i.e. on the continuous level) in the corresponding Sobolev space, reducing the nonlinear boundary-value problem to auxiliary linear problems. We extend earlier results concerning local (Dirichlet) boundary-value problems. We show linear convergence of our method, and present a numerical example.Text17 pages1 file (.pdf)enAttribution 4.0 InternationalNonlocal boundary-value problemsGradient method in Sobolev spaceInfinite-dimensional preconditioningArticle