RT Journal Article
T1 Bivariate delta-evolution equations and convolution polynomials: Computing polynomial expansions of solutions
A1 Alonso Morón, Manuel
A1 Luzón, Ana
AB This paper describes an application of Rota and collaborator's ideas, about the foundation on combinatorial theory, to the computing of solutions of some linear functional partial differential equations. We give a dynamical interpretation of the convolution families of polynomials. Concretely, we interpret them as entries in the matrix representation of the exponentials of certain contractive linear operators in the ring of formal power series. This is the starting point to get symbolic solutions for some functional-partial differential equations. We introduce the bivariate convolution product of convolution families to obtain symbolic solutions for natural extensions of functional-evolution equations related to delta-operators. We put some examples to show how these symbolic methods allow us to get closed formulas for solutions of genuine partial differential equations. We create an adequate framework to base theoretically some of the performed constructions and to get some existence and uniqueness results.
PB Elsevier
SN 0096-3003
YR 2011
FD 2011-10-15
LK https://hdl.handle.net/20.500.14352/42119
UL https://hdl.handle.net/20.500.14352/42119
LA eng
NO Luzón, A., y Alonso Morón, M. «Bivariate Delta-Evolution Equations and Convolution Polynomials: Computing Polynomial Expansions of Solutions». Applied Mathematics and Computation, vol. 218, n.o 4, octubre de 2011, pp. 1417-35. DOI.org (Crossref), https://doi.org/10.1016/j.amc.2011.06.024.
NO Directorate General for Higher Education (Portugal)
DS Docta Complutense
RD 6 abr 2025