Advances in Decision Sciences

Advances in Decision Sciences / 2000 / Article

Open Access

Volume 4 |Article ID 841395 | https://doi.org/10.1155/S1173912600000158

B. Tsang, S. W. Taylor, G. C. Wake, "Variational methods for boundary value problems", Advances in Decision Sciences, vol. 4, Article ID 841395, 12 pages, 2000. https://doi.org/10.1155/S1173912600000158

Variational methods for boundary value problems

Abstract

The variational formulation of boundary value problems is valuable in providing remarkably easy computational algorithms as well as an alternative framework with which to prove existence results. Boundary conditions impose constraints which can be annoying from a computational point of view. The question is then posed: what is the most general boundary value problem which can be posed in variational form with the boundary conditions appearing naturally? Special cases of two-point problems in one-dimension and some higher dimensional problems are addressed. There is a deep connection with self-adjointness for the linear case. Further cases under which a Lagrangian may or may not exist are explained.

Copyright © 2000 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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