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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A uniqueness theorem for a boundary value problem
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by Riaz A. Usmani PDF
Proc. Amer. Math. Soc. 77 (1979), 329-335 Request permission

Abstract:

In this paper it is proved that the two-point boundary value problem, namely $({d^{(4)}}/d{x^4} + f)y = g,y(0) - {A_1} = y(1) - {A_2} = y''(0) - {B_1} = y''(1) - {B_2} = 0$, has a unique solution provided ${\inf _x}f(x) = - \eta > - {\pi ^4}$. The given boundary value problem is discretized by a finite difference scheme. This numerical approximation is proved to be a second order convergent process by establishing an error bound using the ${L_2}$-norm of a vector.
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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 77 (1979), 329-335
  • MSC: Primary 34B05; Secondary 65L10
  • DOI: https://doi.org/10.1090/S0002-9939-1979-0545591-4
  • MathSciNet review: 545591