Two-point Taylor expansions and one-dimensional boundary value problems

Authors:
José L. López and Ester Pérez Sinusía

Journal:
Math. Comp. **79** (2010), 2103-2115

MSC (2010):
Primary 34A25, 34B05, 41A58

DOI:
https://doi.org/10.1090/S0025-5718-10-02370-7

Published electronically:
April 29, 2010

MathSciNet review:
2684357

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider second-order linear differential equations in the interval with Dirichlet, Neumann or mixed Dirichlet-Neumann boundary conditions. We consider , , and analytic in a Cassini disk with foci at containing the interval . The two-point Taylor expansion of the solution at the extreme points is used to give a criterion for the existence and uniqueness of solution of the boundary value problem. This method is constructive and provides the two-point Taylor approximation of the solution(s) when it exists.

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Additional Information

**José L. López**

Affiliation:
Departamento de Ingeniería Matemática e Informática, Universidad Pública de Navarra, 31006-Pamplona, Spain

Email:
jl.lopez@unavarra.es

**Ester Pérez Sinusía**

Affiliation:
Departamento de Matemática Aplicada, Universidad de Zaragoza, 50018-Zaragoza, Spain

Email:
ester.perez@unizar.es

DOI:
https://doi.org/10.1090/S0025-5718-10-02370-7

Keywords:
Second-order linear differential equations,
boundary value problem,
Frobenius method,
two-point Taylor expansions

Received by editor(s):
May 5, 2009

Published electronically:
April 29, 2010

Additional Notes:
The Ministerio de Ciencia y Tecnología (REF. MTM2007-63772) and the Gobierno de Navarra (Res. 228/2008) are acknowledged by their financial support. The Department of Theoretical Physics of the University of Zaragoza is also acknowledged by its hospitality.

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.