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 Cn-l(I) into Rn. 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. © 1981 American Mathematical Society.
P. W. Eloe and L. J. Grimm, "Monotone Iteration And Green’s Functions For Boundary Value Problems," Proceedings of the American Mathematical Society, vol. 78, no. 4, pp. 533 - 538, American Mathematical Society, Jan 1980.
The definitive version is available at https://doi.org/10.1090/S0002-9939-1980-0556627-7
Mathematics and Statistics
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01 Jan 1980