|Authors:||Stević, Stevo||Affiliations:||Mathematical Institute of the Serbian Academy of Sciences and Arts||Title:||On a class of systems of rational second-order difference equations solvable in closed form||Journal:||Mathematical Methods in the Applied Sciences||Volume:||43||Issue:||3||First page:||1001||Last page:||1016||Issue Date:||1-Feb-2020||Rank:||M21||ISSN:||0170-4214||DOI:||10.1002/mma.5809||Abstract:||
We show that the following nonlinear system of difference equations (Formula presented.) where parameters a,b,c,d and initial values x−1,x0,y−1,y0 are real numbers, is solvable in closed form, considerably generalizing some recent results. To do this, we use the method of transformation along with several tricks, transforming the system to some known solvable difference equations, by use of which we obtain some closed-form formulas for general solution to the system. The following five cases are considered separately: (1) c=0; (2) d=0; (3) a=0; (4) b=0; and (5) abcd≠0.
|Keywords:||method of transformation | solution in closed form | solvable system | system of difference equations||Publisher:||Wiley|
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