On the existence of three-stage third-order modified Patankar-Runge-Kutta schemes

DOI10.1007/s11075-019-00680-3zbMath1416.65205OpenAlexW2916672411MaRDI QIDQ2316649

Andreas Meister, Stefan Kopecz

Publication date: 6 August 2019

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-019-00680-3

zbMATH Keywords

Runge-Kutta methodsconservationunconditional positivitymodified Patankar-Runge-Kutta schemesMPRK

Mathematics Subject Classification ID

Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (11)

On the Stability of Unconditionally Positive and Linear Invariants Preserving Time Integration Schemes ⋮ On Lyapunov stability of positive and conservative time integrators and application to second order modified Patankar–Runge–Kutta schemes ⋮ On the stability of strong-stability-preserving modified Patankar–Runge–Kutta schemes ⋮ A study of the local dynamics of modified Patankar DeC and higher order modified Patankar–RK methods ⋮ On the dynamics of first and second order GeCo and gBBKS schemes ⋮ Extension of modified Patankar-Runge-Kutta schemes to nonautonomous production-destruction systems based on Oliver's approach ⋮ Arbitrary high-order, conservative and positivity preserving Patankar-type deferred correction schemes ⋮ \textit{GeCo}: geometric conservative nonstandard schemes for biochemical systems ⋮ Two Nonlinear Positivity-Preserving Finite Volume Schemes for Three-Dimensional Heat Conduction Equations on General Polyhedral Meshes ⋮ An arbitrary high order and positivity preserving method for the shallow water equations ⋮ Issues with positivity-preserving Patankar-type schemes

Cites Work

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• A high-order conservative Patankar-type discretisation for stiff systems of production--destruction equations
• On order conditions for modified Patankar-Runge-Kutta schemes
• Unconditionally positive and conservative third order modified Patankar-Runge-Kutta discretizations of production-destruction systems
• Phosphorus Cycles in Lakes and Rivers: Modeling, Analysis, and Simulation
• A detailed view of filaments and sheets in the warm-hot intergalactic medium

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