Gradient Method in Sobolev Spaces for Nonlocal Boundary-value Problems

Date

2000-06-30

Authors

Karatson, Janos

Journal Title

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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

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