Geodesic
Gradient method in Sobolev spaces for nonlocal boundary-value problems
Electronic journal of differential equations, Tome 2000 (2000)
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__a116,
     author = {Kar\'atson,  J.},
     title = {Gradient method in {Sobolev} spaces for nonlocal boundary-value problems},
     journal = {Electronic journal of differential equations},
     year = {2000},
     volume = {2000},
     zbl = {0995.35020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a116/}
}
TY  - JOUR
AU  - Karátson,  J.
TI  - Gradient method in Sobolev spaces for nonlocal boundary-value problems
JO  - Electronic journal of differential equations
PY  - 2000
VL  - 2000
UR  - http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a116/
LA  - en
ID  - EJDE_2000__2000__a116
ER  - 
%0 Journal Article
%A Karátson,  J.
%T Gradient method in Sobolev spaces for nonlocal boundary-value problems
%J Electronic journal of differential equations
%D 2000
%V 2000
%U http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a116/
%G en
%F EJDE_2000__2000__a116
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__a116/