Journal Article10.1016/0021-9991(72)90039-3
A new method for solving two-point boundary value problems using optimal node distribution
V.E Denny,R.B Landis +1 more
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TL;DR: In this paper, a new method for solving two-point boundary value problems by finite difference methods has been developed, based on the observation that local truncation errors associated with central difference analogues of the defining differential equation become arbitrarily small as the interior node points are arranged in an optimal sequence.
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About: This article is published in Journal of Computational Physics. The article was published on 01 Feb 1972. The article focuses on the topics: Boundary knot method & Finite difference method.
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Citations
Solution of Burner-Stabilized Premixed Laminar Flames by Boundary Value Methods
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Mesh adaptation strategies for problems in fluid dynamics
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The numerical solution of second-order boundary value problems on nonuniform meshes
TL;DR: It is shown that certain commonly used difference schemes yield second-order accurate solutions despite the fact that their truncation error is of lower order, which illuminates a limitation of the standard stability, consistency proof of convergence for difference schemes defined on nonuniform meshes.
Analysis of Optimal Finite Element Meshes in R1
Ivo Babuška,Werner C. Rheinboldt +1 more
TL;DR: For a two-point boundary-value problem the existence of a unique optimal mesh distribution is proved and its properties are analyzed, allowing for rather straightforward extensions to more general problems in one dimension as well as to higher-order elements.
145
Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations
TL;DR: It will be shown that significant economies of execution can be attained if nodes are moved so that they remain concentrated in regions of rapid variation of the flow variables.
142