Electron. J. Diff. Eqns., Vol. 2000(2000), No. 51, pp. 1-17.

Gradient method in Sobolev spaces for nonlocal boundary-value problems

J. Karatson

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
e-mail: karatson@cs.elte.hu

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