William R. McKinney

Works (2)

Updated: July 5th, 2023 16:01

2003 journal article

Numerical approximation of blow-up of radially symmetric solutions of the nonlinear Schrodinger equation

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 25(1), 186–212.

By: G. Akrivis, V. Dougalis, O. Karakashian & W. McKinney*

author keywords: nonlinear Schrodinger equation; point blow-up; finite element methods; adaptive mesh refinement
TL;DR: A numerical method based on a standard Galerkin finite element spatial discretization with piecewise linear, continuous functions and on an implicit Crank--Nicolson type time-stepping procedure is constructed to approximate smooth solutions of the initial-value problem for the radially symmetric nonlinear Schrodin\-ger equation with cubic nonlinearity. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2000 journal article

Stable and unstable solitary-wave solutions of the generalized regularized long-wave equation

JOURNAL OF NONLINEAR SCIENCE, 10(6), 603–638.

By: J. Bona, W. McKinney n & J. Restrepo

author keywords: BBM equation; generalized BBM equation; RLW equation; generalized RLW equation; stable solitary-waves; unstable solitary-waves
TL;DR: It is found that unstable solitary waves may evolve into several, stable solitary waves and that positive initial data need not feature solitary waves at all in its long-time asymptotics. (via Semantic Scholar)
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14. Life Below Water (Web of Science)
Source: Web Of Science
Added: August 6, 2018

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