Eotvos Lorand University
Dept. of Applied Analysis
H-1053, Budapest, Kecskemeti u. 10-12
Hungary
e-mail: karatson@cs.elte.hu
J. Karatson
Abstract:
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.
Submitted November 29, 1999. Published June 30, 2000.
Math Subject Classifications: 35J65, 46N20, 49M10.
Key Words: nonlocal boundary-value problems, gradient method in
Sobolev space, infinite-dimensional preconditioning.
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Janos Karatson Eotvos Lorand University Dept. of Applied Analysis H-1053, Budapest, Kecskemeti u. 10-12 Hungary e-mail: karatson@cs.elte.hu |
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