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The quasilinearization method on an unbounded domain
Author(s):
Paul
W.
Eloe
Journal:
Proc. Amer. Math. Soc.
131
(2003),
1481-1488.
MSC (1991):
Primary 34B40, 34A45
Posted:
September 20, 2002
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Abstract:
We apply a method of quasilinearization to a boundary value problem for an ordinary differential equation on an unbounded domain. A uniquely determined Green's function, which is integrable and of fixed sign, is employed. The hypotheses to apply the quasilinearization method imply uniqueness of solutions. The quasilinearization method generates a bilateral iteration scheme in which the iterates converge monotonically and quadratically to the unique solution.
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Additional Information:
Paul
W.
Eloe
Affiliation:
Department of Mathematics, University of Dayton, Dayton, Ohio 45469-2316
Email:
Paul.Eloe@notes.udayton.edu
DOI:
10.1090/S0002-9939-02-06654-6
PII:
S 0002-9939(02)06654-6
Keywords:
Quasilinearization,
quadratic convergence,
upper and lower solutions,
singular boundary value problems
Received by editor(s):
August 10, 2001
Received by editor(s) in revised form:
December 11, 2001
Posted:
September 20, 2002
Communicated by:
Carmen C. Chicone
Copyright of article:
Copyright
2002,
American Mathematical Society
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