Gradient Method in Sobolev Spaces for Nonlocal Boundary-value Problems
Date
2000-06-30
Authors
Karatson, Janos
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
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.
Description
Keywords
Nonlocal boundary-value problems, Gradient method in Sobolev space, Infinite-dimensional preconditioning
Citation
Karatson, J. (2000). Gradient method in Sobolev spaces for nonlocal boundary-value problems. <i>Electronic Journal of Differential Equations, 2000</i>(51), pp. 1-17.
Rights
Attribution 4.0 International