cite Ortleb & Hundsdorfer 2017

Author: SKopecz

paper/paper.bib

@@ -464,4 +464,19 @@ @article {Izgin2025
   MRNUMBER = {4873114},
   DOI = {10.2140/camcos.2025.20.29},
   URL = {https://doi.org/10.2140/camcos.2025.20.29},
+}
+
+@article{Ortleb2017,
+  author = {Ortleb, Sigrun and Hundsdorfer, Willem},
+  title = {Patankar-type Runge-Kutta schemes for linear PDEs},
+  journal = {AIP Conference Proceedings},
+  volume = {1863},
+  number = {1},
+  pages = {320008},
+  year = {2017},
+  month = {07},
+  issn = {0094-243X},
+  doi = {10.1063/1.4992489},
+  url = {https://doi.org/10.1063/1.4992489},
+  eprint = {https://pubs.aip.org/aip/acp/article-pdf/doi/10.1063/1.4992489/13749027/320008\_1\_online.pdf},
 }

paper/paper.md

@@ -41,8 +41,7 @@ The only standard scheme with which unconditional positivity can be achieved is
 (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 in between 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 have been introduced in recent years, see @burchard2003, @Bruggeman2007, @Broekhuizen2008, @Formaggia2011, @kopeczmeister2018order2, @kopeczmeister2018order3, @huang2019order2, @huang2019order3, @OeffnerTorlo2020, @Martiradonna2020, @Avila2020, @Avila2021, @Blanes2022, @Zhu2024, @Izzo2025, @Izgin2025.  
-Among these, most of the literature is devoted to modified Patankar--Runge--Kutta (MPRK) methods.
+Consequently, various new, unconditionally positive schemes have been introduced in recent years, see @burchard2003, @Bruggeman2007, @Broekhuizen2008, @Formaggia2011, @Ortleb2017, @kopeczmeister2018order2, @kopeczmeister2018order3, @huang2019order2, @huang2019order3, @OeffnerTorlo2020, @Martiradonna2020, @Avila2020, @Avila2021, @Blanes2022, @Zhu2024, @Izzo2025, @Izgin2025. Among these, most of the literature is devoted to modified Patankar--Runge--Kutta (MPRK) methods.
 
 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 aims at making these methods available and thus usable and comparable.