On the numerical solution of a nonlocal boundary value problem. (English) Zbl 1323.65086
Summary: We study a nonlinear boundary value problem involving a nonlocal (integral) operator in the coefficients of the unknown function. Provided sufficient conditions for the existence and uniqueness of the solution, for its approximation, we propose a numerical method consisting of a classical discretization of the problem and an algorithm to solve the resulting nonlocal and nonlinear algebraic system by means of some iterative procedures. The second order of convergence is assured by different sufficient conditions, which can be alternatively used in dependence on the given data. The theoretical results are confirmed by several numerical tests.
MSC:
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
| 65L12 | Finite difference and finite volume methods for ordinary differential equations |
| 65R20 | Numerical methods for integral equations |
| 45J05 | Integro-ordinary differential equations |
Keywords:
nonlocal problems; integro-differential boundary value problems; finite differences methods; nonlocal algebraic systems; iterative methods for solving nonlocal systems; nonlinear boundary value problem; algorithm; convergence; numerical testReferences:
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