On theoretical upper limits for valid timesteps of implicit ODE methods

• Published in: AIMS mathematics Vol. 4; no. 6; pp. 1841 - 1853
• Main Authors: R. Green, Kevin, W. Patrick, George, J. Spiteri, Raymond
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2019
• Subjects: bifurcation; double pendulum; implicit method; initial-value problem
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2019.6.1841

Implicit methods for the numerical solution of initial-value problems may admit multiple solutions at any given time step. Accordingly, their nonlinear solvers may converge to any of these solutions. Below a critical timestep, exactly one of the solutions (the consistent solution) occurs on a soluti...