Geodesic
Gradient method in Sobolev spaces for nonlocal boundary-value problems
Electronic Journal of Differential Equations, Tome 2000 (2000).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: An 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.
Classification : 35J65, 46N20, 49M10
Keywords: nonlocal boundary-value problems, gradient method in Sobolev space, infinite-dimensional preconditioning 
@article{EJDE_2000__2000__a189,
     author = {Kar\'atson, J.},
     title = {Gradient method in {Sobolev} spaces for nonlocal boundary-value problems},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2000},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a189/}
}
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Karátson, J. Gradient method in Sobolev spaces for nonlocal boundary-value problems. Electronic Journal of Differential Equations, Tome 2000 (2000). http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a189/