Gradient Method in Sobolev Spaces for Nonlocal Boundary-value Problems
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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.
CitationKaratson, J. (2000). Gradient method in Sobolev spaces for nonlocal boundary-value problems. Electronic Journal of Differential Equations, 2000(51), pp. 1-17.
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