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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Generalized quasilinearization method
for a second order ordinary differential
equation with Dirichlet boundary conditions


Author: Juan J. Nieto
Journal: Proc. Amer. Math. Soc. 125 (1997), 2599-2604
MSC (1991): Primary 34A45, 34B15
DOI: https://doi.org/10.1090/S0002-9939-97-03976-2
MathSciNet review: 1402880
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Abstract: We study the existence and approximation of solutions for a nonlinear second order ordinary differential equation with Dirichlet boundary value conditions. We present a generalized quasilinearization technique to obtain a sequence of approximate solutions converging quadratically to a solution.


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Additional Information

Juan J. Nieto
Affiliation: Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, Spain
Email: amnieto@usc.es

DOI: https://doi.org/10.1090/S0002-9939-97-03976-2
Keywords: Dirichlet problem, generalized quasilinearization, quadratic convergence
Received by editor(s): March 13, 1996
Additional Notes: The author’s research was partially supported by D.G.I.C.Y.T. (Spain), project PB94-0610, and by EC Network, CHRX-CT94-0555
Communicated by: Hal L. Smith
Article copyright: © Copyright 1997 American Mathematical Society