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Journal of Engineering Mathematics

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01-10-2013

Exact treatment of operator difference equations with nonconstant and noncommutative coefficients

Authors: Maria Anastasia Jivulescu, Antonino Messina

Published in: Journal of Engineering Mathematics | Issue 1/2013

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Abstract

We study a homogeneous linear second-order difference equation with nonconstant and noncommuting operator coefficients in a vector space. We build its exact resolutive formula consisting of the explicit noniterative expression of a generic term of the unknown sequence of vectors. Some nontrivial applications are reported in order to show the usefulness and the broad applicability of the result.

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Kelley WG, Peterson AC (2001) Difference equations. In: An introduction with applications, 2nd edn. Harcourt/Academic, Waltham

Driver RD (1977) Ordinary and delay differential equations. Springer, New YorkCrossRefMATH

Azad H, Laradji A, Mustafa MT (2011) Polynomial solutions of differential equations. Adv Differ Equ 58:1–12MathSciNet

Mallik R (1997) On the solution of a second order linear homogeneous difference equation with variable coefficients. J Math Anal Appl 215(1):32–47MathSciNetCrossRefMATH

Mallik R (1998) Solutions of linear difference equations with variable coeffcients. J Math Anal Appl 222:79–91MathSciNetCrossRefMATH

Napoli A, Messina A, Tretynyk V (2002) Construction of a fundamental set of solutions of an arbitrary homogeneous linear difference equation. Report Math Phys 49(2–3):31–323MathSciNet

Taher RB, Rachidi M (2001) Linear recurrence relations in the algebra of matrices and applications. Linear algebra appl 330:15–24MathSciNetCrossRefMATH

Jivulescu MA, Messina A, Napoli A (2008) Elementary symmetric functions of two solvents of a quadratic matrix equations. Report Math Phys 62(3):411–429MathSciNet

Jivulescu MA, Messina A, Napoli A (2010) General solution of a second order non-homogenous linear difference equation with noncommutative coefficients. Appl Math Inform Sci 4(1):1–14MathSciNetMATH

10.

Jivulescu MA, Messina A, Napoli A, Petruccione F (2007) Exact treatment of linear difference equations with noncommutative coefficients. Math Methods Appl Sci 30:2147–2153MathSciNetCrossRefMATH

11.

Spiegel M (1998) Schaum’s mathematical handbook of formulas and tables. McGraw-Hill, New York, p 11

Title: Exact treatment of operator difference equations with nonconstant and noncommutative coefficients
Authors: Maria Anastasia Jivulescu
Antonino Messina
Publication date: 01-10-2013
Publisher: Springer Netherlands
Published in: Journal of Engineering Mathematics / Issue 1/2013
Print ISSN: 0022-0833
Electronic ISSN: 1573-2703
DOI: https://doi.org/10.1007/s10665-012-9602-9

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