The use of two-point Taylor expansions in singular one-dimensional boundary value problems I

Ferreira, C. (Universidad de Zaragoza) ; López, J.L. ; Pérez Sinusía, E. (Universidad de Zaragoza)

Resumen: We consider the second-order linear differential equation (x+1)y¿+f(x)y'+g(x)y=h(x) in the interval (-1, 1) with initial conditions or boundary conditions (Dirichlet, Neumann or mixed Dirichlet–Neumann). The functions f(x), g(x) and h(x) are analytic in a Cassini disk Dr with foci at x=±1 containing the interval [-1, 1]. Then, the end point of the interval x=-1 may be a regular singular point of the differential equation. The two-point Taylor expansion of the solution y(x) at the end points ±1 is used to study the space of analytic solutions in Dr of the differential equation, and to give a criterion for the existence and uniqueness of analytic solutions of the boundary value problem. This method is constructive and provides the two-point Taylor approximation of the analytic solutions when they exist.

Idioma: Inglés

DOI: 10.1016/j.jmaa.2018.03.041

Año: 2018

Publicado en: Journal of Mathematical Analysis and Applications 463, 2 (2018), 708-725
ISSN: 0022-247X

Factor impacto JCR: 1.188 (2018)

Categ. JCR: MATHEMATICS rank: 65 / 313 = 0.208 (2018) - Q1 - T1
Categ. JCR: MATHEMATICS, APPLIED rank: 117 / 254 = 0.461 (2018) - Q2 - T2

Factor impacto SCIMAGO: 0.966 - Applied Mathematics (Q2) - Analysis (Q2)

Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2014-52859-P

Tipo y forma: Article (PostPrint)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)