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

Special Matrices (2013)

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

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topN. 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 -

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