A numerical method for a nonlocal elliptic boundary value problem. (English) Zbl 1149.65099

Cannon, J. R.; Galiffa, D. J.

J. Integral Equations Appl. 20, No. 2, 243-261 (2008).

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.

Reviewer: Vladimir Gorbunov (Ul’yanovsk)

MSC:

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

Keywords:

integro-ordinary differential equations; existence; uniqueness; difference scheme

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