๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Some aspects of the one-dimensional version of the method of fundamental solutions

โœ Scribed by Y.-S. Smyrlis; A. Karageorghis; G. Georgiou

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
472 KB
Volume
41
Category
Article
ISSN
0898-1221

No coin nor oath required. For personal study only.

โœฆ Synopsis

The method of fundamental solutions (MFS) is a well-established boundary-type numerical method for the solution of certain two-and three-dimensional elliptic boundary value problems [1,2]. The basic ideas were introduced by Kupradze and Alexidze (see, e.g., [3]), whereas the present form of the MFS was proposed by Mathon and Johnston [4]. The aim of this work is to investigate the one-dimensionai analogue of the MFS for the solution of certain two-point boundary value problems.

In particular, the one-dimensional MFS is formulated in the case of linear scalar ordinary differential equations of even degree with constant coefficients. A mathematical justification for the method is provided and various aspects related to its applicability from both an analytical and a numerical standpoint are examined. (~) 2001 Elsevier Science Ltd. All rights reserved.

๐Ÿ“œ SIMILAR VOLUMES

One version of the multigrid method
One version of the multigrid method
โœ V. P. Il'in ๐Ÿ“‚ Article ๐Ÿ“… 1985 ๐Ÿ› SP MAIK Nauka/Interperiodica ๐ŸŒ English โš– 397 KB
The fundamental groups of one-dimensiona
The fundamental groups of one-dimensional spaces
โœ Katsuya Eda; Kazuhiro Kawamura ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 688 KB

Let X be a space of dimension at most I. Then, the fundamental group is isomorphic to a subgroup of the first Tech homotopy group based on finite open covers. Consequently, for a onedimensional continuum X, the fundamental group is isomorphic to a subgroup of the first Tech homotopy group.