An improvement on the positivity results for 2-stage explicit Runge-Kutta methods

DOI10.1016/j.cam.2010.05.020zbMath1203.65110OpenAlexW1966024370MaRDI QIDQ711236

D. Kharzeev

Publication date: 25 October 2010

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.2010.05.020

zbMATH Keywords

monotonicitynumerical resultspositivityinitial value problemsRunge-Kutta methodsEuler methodadvection equationHeun's method

Mathematics Subject Classification ID

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)

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Cites Work

• Unnamed Item
• Positivity for explicit two-step methods in linear multistep and one-leg form
• Selective monotonicity preservation in scalar advection
• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• Positivity of Runge-Kutta and diagonally split Runge-Kutta methods
• The positivity of low-order explicit Runge-Kutta schemes applied in splitting methods.
• Stepsize Conditions for Boundedness in Numerical Initial Value Problems
• Stepsize Conditions for General Monotonicity in Numerical Initial Value Problems
• Total-Variation-Diminishing Time Discretizations
• Second Derivative Extended Backward Differentiation Formulas for the Numerical Integration of Stiff Systems
• Monotonicity-Preserving Linear Multistep Methods

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