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A numerical method for a nonlocal elliptic boundary value problem. (English) Zbl 1149.65099
The problem under consideration is \[ -\alpha\left(\int_0^1{u(t)\,dt}\right)u''=f(x),\; 0<x<1,\, u(0)=a, \, u(1)=b, \] where \(\alpha(\cdot)\) is a positive function. The existence and uniqueness of the solution, weak as well as classical, of the problem are proved at different assumptions with respect to the problem data. The numerical problem via a finite difference scheme is investigated. Three numerical examples demonstrate the proposed method.

65R20 Numerical methods for integral equations
45J05 Integro-ordinary differential equations
45G10 Other nonlinear integral equations
Full Text: DOI
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