Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Total-variation-diminishing time discretizations
SIAM Journal on Scientific and Statistical Computing
Positivity of Runge-Kutta and diagonally split Runge-Kutta methods
Applied Numerical Mathematics - Selected papers on eighth conference on the numerical treatment of differential equations 1-5 September 1997, Alexisbad, Germany
Stepsize Conditions for General Monotonicity in Numerical Initial Value Problems
SIAM Journal on Numerical Analysis
Selective monotonicity preservation in scalar advection
Journal of Computational Physics
Stepsize Conditions for Boundedness in Numerical Initial Value Problems
SIAM Journal on Numerical Analysis
Strong Stability for Runge---Kutta Schemes on a Class of Nonlinear Problems
Journal of Scientific Computing
Hi-index | 7.29 |
In this paper, we investigate the positivity property for a class of 2-stage explicit Runge-Kutta (RK2) methods of order two when applied to the numerical solution of special nonlinear initial value problems (IVPs) for ordinary differential equations (ODEs). We also pay particular attention to monotonicity property. We obtain new results for positivity which are important in practical applications. We provide some numerical examples to illustrate our results.