On the numerical solution of some nonlinear and nonlocal boundary value problems

W. Themistoclakis and A. Vecchio

Applied Mathematics and Computation, 2015, vol. 255, issue C, 135-146

Abstract: The modeling of various physical questions often leads to nonlinear boundary value problems involving a nonlocal operator, which depends on the unknown function in the entire domain, rather than at a single point. In order to answer an open question posed by J.R. Cannon and D.J. Galiffa, we study the numerical solution of a special class of nonlocal nonlinear boundary value problems, which involve the integral of the unknown solution over the integration domain. Starting from Cannon and Galiffa’s results, we provide other sufficient conditions for the unique solvability and a more general convergence theorem. Moreover, we suggest different iterative procedures to handle the nonlocal nonlinearity of the discrete problem and show their performances by some numerical tests.

Keywords: Nonlocal problems; Nonlinear problems; Integro-differential boundary value problems; Numerical iterative methods; Fixed point theory; M-matrices (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:255:y:2015:i:c:p:135-146

DOI: 10.1016/j.amc.2014.08.004

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