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2013 | 1 | 42-48
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
1
Strony
42-48
Opis fizyczny
Daty
otrzymano
2013-10-20
zaakceptowano
2013-11-21
online
2013-12-10
Twórcy
Bibliografia
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  • [11] R.C. McOwen, Partial Differential Equations: Methods and Applications, Prentice Hall, Upper Saddle River, 2002.
  • [12] W.H. Neven and C. Praagman, Column reduction of polynomial matrices, Linear Algebra Appl. 188 (1993), 569–589.
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  • [14] A. Sami Bataineh, M.S.M. Noorani and I. Hashim, Approximate analytical solutions of systems of PDEs by homotopyanalysis method, Comput. Math. Appl. 55 (2008), 2913–2923.[WoS]
  • [15] N. Shayanfar and M. Hadizadeh, Splitting a linear system of operator equations with constant coefficients: A matrixpolynomial approach, Filomat 27(8) (2013), 1447–1454.
  • [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.
  • [17] A.M. Wazwaz, The decomposition method applied to systems of partial diferential equations and to the reactiondiffusion Brusselator model, Appl. Math. Comput. 110 (2000), 251–264.
  • [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]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_spma-2013-0007
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