Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 51, pp. 1-17.

Title: Gradient method in Sobolev spaces for nonlocal boundary-value problems

Author: J. Karatson (Eotvos Lorand Univ., Budapest, Hungary)
         
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.