Open AccessPROPERTIES OF A DIFFERENTIAL SEQUENCE BASED UPON THE KUMMER-SCHWARZ EQUATION
Author(s) -
Aneshkumar Maharaj,
K. Andriopoulos,
P. G. L. Leach
Publication year - 2020
Publication title -
acta polytechnica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.207
H-Index - 15
eISSN - 1805-2363
pISSN - 1210-2709
DOI - 10.14311/ap.2020.60.0428
Subject(s) - sequence (biology) , mathematics , singularity , homogeneous space , riccati equation , order (exchange) , differential equation , exact sequence , recursion (computer science) , generator (circuit theory) , pure mathematics , mathematical analysis , physics , algorithm , geometry , finance , economics , biology , power (physics) , quantum mechanics , genetics
In this paper, we determine a recursion operator for the Kummer-Schwarz equation, which leads to a sequence with unacceptable singularity properties. A different sequence is devised based upon the relationship between the Kummer-Schwarz equation and the first-order Riccati equation for which a particular generator has been found to give interesting and excellent properties. We examine the elements of this sequence in terms of the usual properties to be investigated – symmetries, singularity properties, integrability, alternate sequence – and provide an explanation of the curious relationship between the results of the singularity analysis and a consideration of the solution of each element obtained by quadratures.