Comparison of boundedness and monotonicity properties of one-leg and linear multistep methods

DOI10.1016/j.cam.2014.10.025zbMath1306.65228OpenAlexW2013213909MaRDI QIDQ482681

A. Mozartova, Igor Savostianov, Willem H. Hundsdorfer

Publication date: 6 January 2015

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2014.10.025

zbMATH Keywords

monotonicityboundednessinitial value problemmethod of linesmultistep methodsstrong-stability-preservingone-leg method

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Uses Software

• RODAS

Cites Work

• Stepsize restrictions for boundedness and monotonicity of multistep methods
• Special boundedness properties in numerical initial value problems
• Positivity for explicit two-step methods in linear multistep and one-leg form
• Contractivity of Runge-Kutta methods
• Stepsize Conditions for Boundedness in Numerical Initial Value Problems
• Solving Ordinary Differential Equations I
• On monotonicity and boundedness properties of linear multistep methods
• Stepsize Conditions for General Monotonicity in Numerical Initial Value Problems
• Monotonicity-Preserving Linear Multistep Methods
• An extension and analysis of the Shu-Osher representation of Runge-Kutta methods
• Representations of Runge--Kutta Methods and Strong Stability Preserving Methods
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