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Ordinary and generalized Green’s functions for the second order discrete nonlocal problems. (English) Zbl 1338.65198

Summary: In this paper, we investigate the properties of a generalized Green’s function describing the minimum norm least squares solution for a second order discrete problem with two nonlocal conditions. The properties obtained of a generalized Green’s function resemble analogous properties of an ordinary Green’s function that describes the unique exact solution if it exists. Several features are illustrated by examples.

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B27 Green’s functions for ordinary differential equations
65L08 Numerical solution of ill-posed problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations

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References:

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