# On network models and the symbolic solution of network equations

• Volume: 11, Issue: 1, page 237-269
• ISSN: 1641-876X

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## Abstract

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This paper gives an overview of the formulation and solution of network equations, with emphasis on the historical development of this area. Networks are mathematical models. The three ingredients of network descriptions are discussed. It is shown how the network equations of one-dimensional multi-port networks can be formulated and solved symbolically. If necessary, the network graph is modified so as to obtain an admittance representation for all kinds of multi-ports. N-dimensional networks are defined as graphs with the algebraic structure of N-dimensional vectors. In civil engineering, framed structures in two and three spatial dimensions can be modeled as 3-dimensional or 6-dimensional networks. The separation of geometry from topology is a characteristic feature of such networks.

## How to cite

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Reinschke, Kurt. "On network models and the symbolic solution of network equations." International Journal of Applied Mathematics and Computer Science 11.1 (2001): 237-269. <http://eudml.org/doc/207502>.

@article{Reinschke2001,
abstract = {This paper gives an overview of the formulation and solution of network equations, with emphasis on the historical development of this area. Networks are mathematical models. The three ingredients of network descriptions are discussed. It is shown how the network equations of one-dimensional multi-port networks can be formulated and solved symbolically. If necessary, the network graph is modified so as to obtain an admittance representation for all kinds of multi-ports. N-dimensional networks are defined as graphs with the algebraic structure of N-dimensional vectors. In civil engineering, framed structures in two and three spatial dimensions can be modeled as 3-dimensional or 6-dimensional networks. The separation of geometry from topology is a characteristic feature of such networks.},
author = {Reinschke, Kurt},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {history of network theory; multidimensional networks; network equations; network graphs; admittance representation of multi-ports; modified nodal analysis; admittance representation of multiports},
language = {eng},
number = {1},
pages = {237-269},
title = {On network models and the symbolic solution of network equations},
url = {http://eudml.org/doc/207502},
volume = {11},
year = {2001},
}

TY - JOUR
AU - Reinschke, Kurt
TI - On network models and the symbolic solution of network equations
JO - International Journal of Applied Mathematics and Computer Science
PY - 2001
VL - 11
IS - 1
SP - 237
EP - 269
AB - This paper gives an overview of the formulation and solution of network equations, with emphasis on the historical development of this area. Networks are mathematical models. The three ingredients of network descriptions are discussed. It is shown how the network equations of one-dimensional multi-port networks can be formulated and solved symbolically. If necessary, the network graph is modified so as to obtain an admittance representation for all kinds of multi-ports. N-dimensional networks are defined as graphs with the algebraic structure of N-dimensional vectors. In civil engineering, framed structures in two and three spatial dimensions can be modeled as 3-dimensional or 6-dimensional networks. The separation of geometry from topology is a characteristic feature of such networks.
LA - eng
KW - history of network theory; multidimensional networks; network equations; network graphs; admittance representation of multi-ports; modified nodal analysis; admittance representation of multiports
UR - http://eudml.org/doc/207502
ER -

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