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Preservation of Lyapunov stability through effective discretization in Runge–Kutta method
Priscila F.S. Guedes, Eduardo M.A.M. Mendes, Erivelton Nepomuceno and Marcio J. Lacerda Chaos, Solitons & Fractals 193 116084 (2025) https://doi.org/10.1016/j.chaos.2025.116084
Order conditions for Runge–Kutta-like methods
with solution-dependent coefficients
Thomas Izgin, David I. Ketcheson and Andreas Meister Communications in Applied Mathematics and Computational Science 20(1) 29 (2025) https://doi.org/10.2140/camcos.2025.20.29
A high-order, fully well-balanced, unconditionally positivity-preserving finite volume framework for flood simulations
Mirco Ciallella, Lorenzo Micalizzi, Victor Michel-Dansac, Philipp Öffner and Davide Torlo GEM - International Journal on Geomathematics 16(1) (2025) https://doi.org/10.1007/s13137-025-00262-7
On the non-global linear stability and spurious fixed points of MPRK schemes with negative RK parameters
On the stability of strong-stability-preserving modified Patankar–Runge–Kutta schemes
Juntao Huang, Thomas Izgin, Stefan Kopecz, Andreas Meister and Chi-Wang Shu ESAIM: Mathematical Modelling and Numerical Analysis 57(2) 1063 (2023) https://doi.org/10.1051/m2an/2023005
A Stability Analysis of Modified Patankar–Runge–Kutta methods for a nonlinear Production–Destruction System