Monotone iteration and Green’s functions for boundary value problems

Eloe, P. W.; Grimm, L. J.

doi:10.1090/S0002-9939-1980-0556627-7

Monotone iteration and Green’s functions for boundary value problems
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by P. W. Eloe and L. J. Grimm PDF

Proc. Amer. Math. Soc. 78 (1980), 533-538 Request permission

Abstract:

An iteration scheme is given for approximating solutions of boundary problems of the form $Ly = f(x,y),Ty(x) = r$, where L is an nth order linear differential operator, f is continuous and T is a continuous linear operator from ${C^{n - 1}}(I)$ into ${{\mathbf {R}}^n}$. The scheme is based on the condition that the Green’s function $G(x,s)$ for the associated linear problem $Ly = 0,Ty = 0$ exists and has sign independent of s.

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