additional references

Author: ranocha

paper/paper.bib

@@ -252,3 +252,52 @@ @article{christ2023plots
   eprinttype={arxiv},
   eprintclass={cs.GR}
 }
+
+@article{nusslein2021positivity,
+  title={Positivity-Preserving Adaptive {R}unge-{K}utta Methods},
+  author={N\"u{\ss}lein, Stephan and Ranocha, Hendrik and Ketcheson, David I},
+  journal={Communications in Applied Mathematics and Computational Science},
+  year={2021},
+  month={11},
+  doi={10.2140/camcos.2021.16.155},
+  volume={16},
+  number={2},
+  pages={155--179},
+  eprint={2005.06268},
+  eprinttype={arxiv},
+  eprintclass={math.NA}
+}
+
+@article{sandu2001positive,
+  title={Positive numerical integration methods for chemical
+         kinetic systems},
+  author={Sandu, Adrian},
+  journal={Journal of Computational Physics},
+  volume={170},
+  number={2},
+  pages={589--602},
+  year={2001},
+  publisher={Elsevier},
+  doi={10.1006/jcph.2001.6750}
+}
+
+@article{bolley1978conservation,
+  title={Conservation de la positivit{\'e} lors de la discr{\'e}tisation
+         des probl{\`e}mes d'{\'e}volution paraboliques},
+  author={Bolley, Catherine and Crouzeix, Michel},
+  journal={RAIRO. Analyse num{\'e}rique},
+  volume={12},
+  number={3},
+  pages={237--245},
+  year={1978},
+  publisher={EDP Sciences}
+}
+
+@book{gottlieb2011strong,
+  title={Strong stability preserving {R}unge-{K}utta and multistep time
+         discretizations},
+  author={Gottlieb, Sigal and Ketcheson, David I and Shu, Chi-Wang},
+  year={2011},
+  publisher={World Scientific},
+  address={Singapore}
+}

paper/paper.md

@@ -36,9 +36,10 @@ Many systems of ordinary differential equations that model real-life application
 For some of these systems unconditionally positivity-preserving time integration methods are helpful or even necessary to obtain meaningful solutions. 
 
 Unfortunately, positivity is a property that almost all standard time integration schemes, such as Runge–Kutta methods, Rosenbrock methods, or linear multistep methods, do not preserve.
+In particular, higher-order general linear methods cannot preserve positivity unconditionally [@bolley1978conservation].
 The only standard scheme with which unconditional positivity can be achieved is the implicit Euler method
 (assuming that the nonlinear systems are solved exactly). However, this is only first-order accurate and, in addition, the preservation of positivity within the nonlinear iteration process poses a problem. 
-Another strategy for preserving positivity used in existing open source or commercial packages (like MATLAB) is to set negative solution components that are accepted by the step size control to zero. Unfortunately, this can have a negative impact on possible conservation properties. Further approaches in the literature include projections inbetween time steps, if a negative solution was computed, or it is tried to reduce the time step size as long as a non-negative solution is calculated. Finally, strong stability preserving (SSP) methods can also be used to preserve positivity, but this is again subject to step size limitations. 
+Another strategy for preserving positivity used in existing open source or commercial packages (like MATLAB) is to set negative solution components that are accepted by the step size control to zero. Unfortunately, this can have a negative impact on possible conservation properties. Further approaches in the literature include projections inbetween time steps [@sandu2001positive,@nusslein2021positivity], if a negative solution was computed, or it is tried to reduce the time step size as long as a non-negative solution is calculated. Finally, strong stability preserving (SSP) methods can also be used to preserve positivity, but this is again subject to step size limitations [@gottlieb2011strong]. 
 
 Consequently, various new, unconditionally positive schemes, especially modified Patankar--Runge--Kutta (MPRK) methods, have been introduced in recent years.
 Unfortunately, these new methods are not yet available in software packages, making them inaccessible to most users and limiting their comparability within the scientific community. PositiveIntegrators.jl makes these methods available and thus usable and comparable.