Abstract:
We consider a variant of the Cauchy problem for a multidimensional difference equation with constant coefficients, which connected with a lattice path problem in enumerative combinatorial analysis. We obtained a formula in which generating function of the solution to the Cauchy problem is expressed in terms of generating functions of the Cauchy data and a formula expressing solution to the Cauchy problem through its fundamental solution and Cauchy data.
Keywords:
difference equation, fundamental solution, generating function, Dyck paths.
Funding agency
This work of author was financed by the PhD SibFU grant for support of scientific research no. 14.
Received: 21.12.2019 Received in revised form: 26.01.2020 Accepted: 03.02.2020
Bibliographic databases:
Document Type:
Article
UDC:517.55+517.962.26
Language: English
Citation:
Alexander P. Lyapin, Sreelatha Chandragiri, “The Cauchy problem for multidimensional difference equations in lattice cones”, J. Sib. Fed. Univ. Math. Phys., 13:2 (2020), 187–196
Sreelatha Chandragiri, “Counting lattice paths by using difference equations with non-constant coefficients”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 44 (2023), 55–70
Luis M. Sánchez-Ruiz, Sanjib Kumar Datta, Nityagopal Biswas, Matilde Legua, “Picturing the Growth Order of Solutions in Complex Linear Differential–Difference Equations with Coefficients of φ-Order”, Axioms, 12:3 (2023), 239
A. P. Lyapin, T. Cuchta, “Sections of the generating series of a solution to a difference equation in a simplicial cone”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 42 (2022), 75–89
A. P. Lyapin, S. S. Akhtamova, “Rekurrentnye sootnosheniya dlya sechenii proizvodyaschego ryada resheniya mnogomernogo raznostnogo uravneniya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 31:3 (2021), 414–423
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