Total-variation-diminishing time discretizations
SIAM Journal on Scientific and Statistical Computing
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Representations of Runge-Kutta Methods and Strong Stability Preserving Methods
SIAM Journal on Numerical Analysis
High-order linear multistep methods with general monotonicity and boundedness properties
Journal of Computational Physics
IMEX extensions of linear multistep methods with general monotonicity and boundedness properties
Journal of Computational Physics
Stepsize Conditions for General Monotonicity in Numerical Initial Value Problems
SIAM Journal on Numerical Analysis
High Order Strong Stability Preserving Time Discretizations
Journal of Scientific Computing
Stepsize Conditions for Boundedness in Numerical Initial Value Problems
SIAM Journal on Numerical Analysis
The existence of stepsize-coefficients for boundedness of linear multistep methods
Applied Numerical Mathematics
Journal of Computational Physics
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In this paper nonlinear monotonicity and boundedness properties are analyzed for linear multistep methods. We focus on methods which satisfy a weaker boundedness condition than strict monotonicity for arbitrary starting values. In this way, many linear multistep methods of practical interest are included in the theory. Moreover, it will be shown that for such methods monotonicity can still be valid with suitable Runge-Kutta starting procedures. Restrictions on the stepsizes are derived that are not only sufficient but also necessary for these boundedness and monotonicity properties.