Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



A uniqueness theorem for a boundary value problem

Author: Riaz A. Usmani
Journal: Proc. Amer. Math. Soc. 77 (1979), 329-335
MSC: Primary 34B05; Secondary 65L10
MathSciNet review: 545591
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34B05, 65L10

Retrieve articles in all journals with MSC: 34B05, 65L10

Additional Information

Keywords: Brouwer's fixed point theorem, Euclidean and $ {L_2}$-norm of a vector, finite difference scheme, local truncation error, plate deflection theory, posteriori error bound, spectral norm of a matrix, two-point boundary value problem
Article copyright: © Copyright 1979 American Mathematical Society