Premium
A comparison of numerical methods for conservative and positive advection‐diffusion‐production‐destruction systems
Author(s) -
Kopecz Stefan,
Meister Andreas
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900209
Subject(s) - ode , advection , time stepping , computation , diffusion , mathematics , contrast (vision) , computer science , scheme (mathematics) , production (economics) , numerical analysis , numerical diffusion , computer simulation , mathematical optimization , mechanics , algorithm , mathematical analysis , physics , simulation , economics , thermodynamics , macroeconomics , artificial intelligence , discretization
Abstract In many simulations it is important to guarantee positivity of the numerical approximations. For standard ODE solvers positivity is usually achieved by restrictions of the time step size, in contrast, MPRK schemes are unconditionally positive, which allows for much faster computations. We compare MPRK schemes and standard ODE solvers applied to an advection‐diffusion‐produ system for which it is essential to avoid negative approximations .