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Update paper/paper.md
Co-authored-by: Joshua Lampert <51029046+JoshuaLampert@users.noreply.github.com>
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@@ -77,7 +77,7 @@ The implemented methods were originally introduced for conservative production-d
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Readers interested in additional theoretical background, further properties of the implemented schemes, and some applications are referred to the publications of @kopeczmeister2019, @izgin2022stability1, @izgin2022stability2, @huang2023, @torlo2022, and @izginoeffner2023. PositiveIntegrators.jl was successfully applied in the work of @bartel2024structure to solve Fokker-Planck equations, ensuring the positivity of the unknown quantities.
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Existing software libraries do not have a strong focus on unconditional positivity and, to the authors' knowledge, there is no other software library which offers MPRK schemes.
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Existing software libraries do not have a strong focus on unconditional positivity and, to the authors' knowledge, there is no other software library offering MPRK schemes.
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A common strategy to obtain nonnegative solutions used in the `PositiveDomain` callback of DifferentialEquations.jl or the commercial package MATLAB is described by @Shampine2005. In this approach negative components of approximate solutions that have been accepted by the adaptive time stepping algorithm are set to zero.
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Another possibility is to reduce the chosen time step size beyond accuracy considerations until a nonnegative approximation is calculated. This can be achieved in DifferentialEquations.jl using the solver option `isoutofdomain`.
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