On a solvable system of difference equations of fourth order

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2013 English Publisher:Elsevier BVJournal:Applied Mathematics and Computation, volume 219, pages 5,706-5,716 (issn: 0096-3003,

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Authors: Stevo Stevic;

doi: 10.1016/j.amc.2012.11.024

On a solvable system of difference equations of fourth order

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Abstract

It is shown that the next system of k difference equationsx"n^(^j^)=a"n^(^j^)x"n"-"k^(^j^)b"n^(^j^)@?"i"="1^kx"n"-"i^(^@s^(^j^+^i^-^1^)^)+c"n^(^j^),n@?N"0,j=1,k@?,where a"n^(^j^),b"n^(^j^),c"n^(^j^),n@?N"0,j=1,k@?, and initial values x"-"i^(^j^),i,j@?{1,...,k}, are real numbers, and where @s:N->{1,...,k} is defined by @s(km+j)=j+1,j=1,k-1@?,@s(km+k)=1, m@?N"0, can be solved in closed form in an elegant way. Some applications of obtained formulas, for the case when the sequences a"n^(^j^),b"n^(^j^) and c"n^(^j^) are k-periodic are also given.

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Serbian Academy of Sciences and Arts
Serbia

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