An approach based on matrix polynomials for linear systems of partial differential equations

N. Shayanfar; M. Hadizadeh

Special Matrices (2013)

  • Volume: 1, page 42-48
  • ISSN: 2300-7451

Abstract

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In this paper, an approach based on matrix polynomials is introduced for solving linear systems of partial differential equations. The main feature of the proposed method is the computation of the Smith canonical form of the assigned matrix polynomial to the linear system of PDEs, which leads to a reduced system. It will be shown that the reduced one is an independent system of PDEs having only one unknown in each equation. A comparison of the results for several test problems reveals that the method is very effective and convenient. The basic idea described in this paper can be employed to solve other linear functional systems.

How to cite

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N. Shayanfar, and M. Hadizadeh. "An approach based on matrix polynomials for linear systems of partial differential equations." Special Matrices 1 (2013): 42-48. <http://eudml.org/doc/266867>.

@article{N2013,
abstract = {In this paper, an approach based on matrix polynomials is introduced for solving linear systems of partial differential equations. The main feature of the proposed method is the computation of the Smith canonical form of the assigned matrix polynomial to the linear system of PDEs, which leads to a reduced system. It will be shown that the reduced one is an independent system of PDEs having only one unknown in each equation. A comparison of the results for several test problems reveals that the method is very effective and convenient. The basic idea described in this paper can be employed to solve other linear functional systems.},
author = {N. Shayanfar, M. Hadizadeh},
journal = {Special Matrices},
keywords = {linear system of partial differential equations; linear operator; matrix polynomial; Smith canonical form; numerical treatment; reduced system},
language = {eng},
pages = {42-48},
title = {An approach based on matrix polynomials for linear systems of partial differential equations},
url = {http://eudml.org/doc/266867},
volume = {1},
year = {2013},
}

TY - JOUR
AU - N. Shayanfar
AU - M. Hadizadeh
TI - An approach based on matrix polynomials for linear systems of partial differential equations
JO - Special Matrices
PY - 2013
VL - 1
SP - 42
EP - 48
AB - In this paper, an approach based on matrix polynomials is introduced for solving linear systems of partial differential equations. The main feature of the proposed method is the computation of the Smith canonical form of the assigned matrix polynomial to the linear system of PDEs, which leads to a reduced system. It will be shown that the reduced one is an independent system of PDEs having only one unknown in each equation. A comparison of the results for several test problems reveals that the method is very effective and convenient. The basic idea described in this paper can be employed to solve other linear functional systems.
LA - eng
KW - linear system of partial differential equations; linear operator; matrix polynomial; Smith canonical form; numerical treatment; reduced system
UR - http://eudml.org/doc/266867
ER -

References

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  15. [15] N. Shayanfar and M. Hadizadeh, Splitting a linear system of operator equations with constant coefficients: A matrix polynomial approach, Filomat 27(8) (2013), 1447–1454. Zbl06451488
  16. [16] N. Shayanfar, M. Hadizadeh and A. Amiraslani, Integral operators acting as variables of the matrix polynomial: application to system of integral equations, Ann. Funct. Anal. 3(2) (2012), 170–182. Zbl1268.47059
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  18. [18] J. Wilkening and J. Yu, A local construction of the Smith normal form of a matrix polynomial, J. Symbolic Comput. 46 (2011), 1–22. [WoS] Zbl1206.65146

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