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Comparison theorems for a third order method

✍ Scribed by J.P. Milaszewicz

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 242 KB
Volume: 10
Category: Article
ISSN: 0893-9659
DOI: 10.1016/s0893-9659(96)00104-8

No coin nor oath required. For personal study only.

✦ Synopsis

It is proved that monotone convergence of a third order bracketing method for nonlinear systems with convexity hypotheses is improved whenever the starting points are chosen corn ponentwise as close to the root as possible.

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## Abstract Utilizing the quadratic functional criteria and positive functionals, the author develops a comparison theorem for oscillation of partial differential equations. This result parallels a comparison of the oscillation of scalar ordinary differential equations to oscillation of vector‐matr