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Title: Implicit Runge-Kutta methods for Lipschitz continuous ordinary differential equations
Authors: Chen, X 
Mahmoud, S
Issue Date: 2008
Source: SIAM journal on numerical analysis, 2008, v. 46, no. 3, p. 1266–1280
Abstract: Implicit Runge–Kutta (IRK) methods for solving the nonsmooth ordinary differential equation (ODE) involve a system of nonsmooth equations. We show superlinear convergence of the slanting Newton method for solving the system of nonsmooth equations. We prove the slanting differentiability and give a slanting function for the involved function. We develop a new code based on the slanting Newton method and the IRK method for nonsmooth ODEs arising from structural oscillation and pounding. We show that the new code is efficient for solving a nonsmooth ODE model for the collapse of the Tacoma Narrows suspension bridge and simulating 13 different earthquakes.
Keywords: Implicit Runge–Kutta method
Slanting Newton method
Nonsmooth equations
Ordinary differential equation
Publisher: Society for Industrial and Applied Mathematics
Journal: SIAM journal on numerical analysis 
ISSN: 0036-1429 (print)
1095-7170 (online)
DOI: 10.1137/070688699
Rights: © 2008 Society for Industrial and Applied Mathematics
Appears in Collections:Journal/Magazine Article

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