Biblioteca de la Universidad Complutense de Madrid

Bivariate delta-evolution equations and convolution polynomials: Computing polynomial expansions of solutions

Impacto

Morón, Manuel A. y Luzón, Ana (2011) Bivariate delta-evolution equations and convolution polynomials: Computing polynomial expansions of solutions. Applied Mathematics and Computation, 218 (4). pp. 1417-1435. ISSN 0096-3003

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URL Oficial: http://www.sciencedirect.com/science/article/pii/S0096300311008514



Resumen

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.


Tipo de documento:Artículo
Palabras clave:Riordan arrays; matrices; Ultrametric; Convolution family; Delta-operator; Riordan group; Delta-evolution equation; Bivariate convolution
Materias:Ciencias > Matemáticas > Álgebra
Código ID:14894
Depositado:19 Abr 2012 09:10
Última Modificación:06 Feb 2014 10:11

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