[DO NOT MERGE] JOSS Paper Draft

.github/workflows/PaperDraft.yml

@@ -0,0 +1,33 @@
+name: Build JOSS paper draft PDF
+
+on:
+  push:
+    paths:
+    - paper/**
+    - .github/workflows/draft-pdf.yml
+  pull_request:
+    paths:
+    - paper/**
+    - .github/workflows/draft-pdf.yml
+
+jobs:
+  paper:
+    runs-on: ubuntu-latest
+    name: JOSS Paper Draft
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v4
+      - name: Build draft PDF
+        uses: openjournals/openjournals-draft-action@master
+        with:
+          journal: joss
+          # This should be the path to the paper within your repo.
+          paper-path: paper/paper.md
+      - name: Upload
+        uses: actions/upload-artifact@v4
+        with:
+          name: paper
+          # This is the output path where Pandoc will write the compiled
+          # PDF. Note, this should be the same directory as the input
+          # paper.md
+          path: paper/paper.pdf

.gitignore

@@ -28,6 +28,6 @@ docs/contributing.md
 # environment.
 Manifest.toml
 
-run
-run/*
+**/run*
 **/*.code-workspace
+**/*.pb.gz

.typos.toml

@@ -0,0 +1,2 @@
+[default.extend-words]
+sigal = "sigal"

paper/paper.bib

@@ -0,0 +1,303 @@
+@article{bartel2024structure,
+  title={Structure-preserving numerical methods for {F}okker-{P}lanck
+         equations},
+  author={Bartel, Hanna and Lampert, Joshua and Ranocha, Hendrik},
+  journal={Proceedings in Applied Mathematics and Mechanics},
+  pages={e202400007},
+  year={2024},
+  month={11},
+  doi={10.1002/pamm.202400007},
+  eprint={2404.07641},
+  eprinttype={arxiv},
+  eprintclass={math.NA}
+}
+
+@article{burchard2003,
+  title={A high-order conservative {P}atankar-type discretisation for
+         stiff systems of production--destruction equations},
+  author={Burchard, Hans and Deleersnijder, Eric and Meister, Andreas},
+  journal={Applied Numerical Mathematics},
+  volume={47},
+  number={1},
+  pages={1--30},
+  year={2003},
+  publisher={Elsevier},
+  doi={10.1016/S0168-9274(03)00101-6}
+}
+
+@article{kopeczmeister2018order2,
+  title={On order conditions for modified {P}atankar-{R}unge-{K}utta
+         schemes},
+  author={Kopecz, Stefan and Meister, Andreas},
+  journal={Applied Numerical Mathematics},
+  volume={123},
+  pages={159--179},
+  year={2018},
+  publisher={Elsevier},
+  doi={10.1016/j.apnum.2017.09.004}
+}
+
+@article {kopeczmeister2018order3,
+  title={Unconditionally positive and conservative third order
+         modified {P}atankar-{R}unge-{K}utta discretizations of
+         production--destruction systems},
+  author={Kopecz, Stefan and Meister, Andreas},
+  journal={BIT Numerical Mathematics},
+  volume={58},
+  number={3},
+  pages={691--728},
+  year={2018},
+  publisher={Springer},
+  doi={10.1007/s10543-018-0705-1}
+}
+
+@article {kopeczmeister2019,
+  title={On the existence of three-stage third-order modified
+         {P}atankar-{R}unge-{K}utta schemes},
+  author={Kopecz, Stefan and Meister, Andreas},
+  journal={Numerical Algorithms},
+  pages={1--12},
+  year={2019},
+  publisher={Springer},
+  doi={10.1007/s11075-019-00680-3}
+}
+
+@article {izgin2022stability1,
+  title={On {L}yapunov stability of positive and conservative
+         time integrators and application to second order modified
+         {P}atankar-{R}unge-{K}utta schemes},
+  author={Izgin, Thomas and Kopecz, Stefan and Meister, Andreas},
+  journal={ESAIM: Mathematical Modelling and Numerical Analysis},
+  volume={56},
+  number={3},
+  pages={1053--1080},
+  year={2022},
+  publisher={EDP Sciences},
+  doi={10.1051/m2an/2022031}}
+}
+
+@article {izgin2022stability2,
+  title={On the stability of unconditionally positive and linear invariants
+         preserving time integration schemes},
+  author={Izgin, Thomas and Kopecz, Stefan and Meister, Andreas},
+  journal={SIAM Journal on Numerical Analysis},
+  volume={60},
+  number={6},
+  pages={3029--3051},
+  year={2022},
+  publisher={SIAM},
+  doi={10.1137/22M1480318}
+}
+
+@article {huang2023,
+  title={On the stability of strong-stability-preserving modified
+         {P}atankar-{R}unge-{K}utta schemes},
+  author={Huang, Juntao and Izgin, Thomas and Kopecz, Stefan and
+          Meister, Andreas and Shu, Chi-Wang},
+  journal={ESAIM: Mathematical Modelling and Numerical Analysis},
+  volume={57},
+  number={2},
+  pages={1063--1086},
+  year={2023},
+  publisher={EDP Sciences},
+  doi={10.1051/m2an/2023005}
+}
+
+
+@article {huang2019order3,
+  title={A Third-Order Unconditionally Positivity-Preserving Scheme for
+         Production-Destruction Equations with Applications to
+         Non-equilibrium Flows},
+  author={Huang, Juntao and Zhao, Weifeng and Shu, Chi-Wang},
+  journal={Journal of Scientific Computing},
+  volume={79},
+  number={2},
+  pages={1015--1056},
+  year={2019},
+  publisher={Springer},
+  doi={10.1007/s10915-018-0881-9}
+}
+
+@article {huang2019order2,
+  title={Positivity-Preserving Time Discretizations for
+         Production-Destruction Equations with Applications to
+         Non-equilibrium Flows},
+  author={Huang, Juntao and Shu, Chi-Wang},
+  journal={Journal of Scientific Computing},
+  volume={78},
+  number={3},
+  pages={1811--1839},
+  year={2019},
+  publisher={Springer},
+  doi={10.1007/s10915-018-0852-1}
+}
+
+@article {torlo2022,
+  title={Issues with Positivity-Preserving {P}atankar-type Schemes},
+  author={Torlo, Davide and \"Offner, Philipp and Ranocha, Hendrik},
+  journal={Applied Numerical Mathematics},
+  year={2022},
+  month={08},
+  volume={182},
+  pages={117--147},
+  doi={10.1016/j.apnum.2022.07.014},
+  eprint={2108.07347},
+  eprinttype={arxiv},
+  eprintclass={math.NA}
+}
+
+@inbook{benzmeister2015,
+  author="Meister, Andreas and Benz, Joachim",
+  editor="Freeden, Willi and Nashed, M. Zuhair and Sonar, Thomas",
+  title="Phosphorus Cycles in Lakes and Rivers: Modeling, Analysis, and Simulation",
+  bookTitle="Handbook of Geomathematics",
+  year="2015",
+  publisher="Springer Berlin Heidelberg",
+  address="Berlin, Heidelberg",
+  pages="1387--1416",
+  isbn="978-3-642-54551-1",
+  doi="10.1007/978-3-642-54551-1_23",
+  url="https://doi.org/10.1007/978-3-642-54551-1_23"
+}
+
+@article {izginoeffner2023,
+  AUTHOR = {Izgin, Thomas and \"Offner, Philipp},
+  TITLE = {A study of the local dynamics of modified {P}atankar {D}e{C}
+              and higher order modified {P}atankar-{RK} methods},
+  journal={ESAIM: Mathematical Modelling and Numerical Analysis},
+  VOLUME = {57},
+  YEAR = {2023},
+  NUMBER = {4},
+  PAGES = {2319--2348},
+  ISSN = {2822-7840,2804-7214},
+  MRCLASS = {65L05 (65L06 65L20)},
+  MRNUMBER = {4612598},
+  DOI = {10.1051/m2an/2023053},
+  URL = {https://doi.org/10.1051/m2an/2023053},
+}
+
+
+@article {OeffnerTorlo2020,
+  AUTHOR = {\"Offner, Philipp and Torlo, Davide},
+  TITLE = {Arbitrary high-order, conservative and positivity preserving
+              {P}atankar-type deferred correction schemes},
+  JOURNAL = {Applied Numerical Mathematics},
+  VOLUME = {153},
+  YEAR = {2020},
+  PAGES = {15--34},
+  ISSN = {0168-9274,1873-5460},
+  MRCLASS = {65L06},
+  MRNUMBER = {4064785},
+  DOI = {10.1016/j.apnum.2020.01.025},
+  URL = {https://doi.org/10.1016/j.apnum.2020.01.025},
+}
+
+@article {Shampine2005,
+  AUTHOR = {Shampine, L. F. and Thompson, S. and Kierzenka, J. A. and
+              Byrne, G. D.},
+  TITLE = {Non-negative solutions of {ODE}s},
+  JOURNAL = {Applied Mathematics and Computation},
+  VOLUME = {170},
+  YEAR = {2005},
+  NUMBER = {1},
+  PAGES = {556--569},
+  ISSN = {0096-3003,1873-5649},
+  MRCLASS = {34C11},
+  MRNUMBER = {2177561},
+  DOI = {10.1016/j.amc.2004.12.011},
+  URL = {https://doi.org/10.1016/j.amc.2004.12.011},
+}
+
+@article{rackauckas2017differentialequations,
+  title={{DifferentialEquations.jl} {--} {A} Performant and Feature-Rich
+         Ecosystem for Solving Differential Equations in {J}ulia},
+  author={Rackauckas, Christopher and Nie, Qing},
+  journal={Journal of Open Research Software},
+  volume={5},
+  number={1},
+  pages={15},
+  year={2017},
+  publisher={Ubiquity Press},
+  doi={10.5334/jors.151}
+}
+
+@article{bezanson2017julia,
+  title={Julia: {A} Fresh Approach to Numerical Computing},
+  author={Bezanson, Jeff and Edelman, Alan and Karpinski, Stefan and
+          Shah, Viral B},
+  journal={SIAM Review},
+  volume={59},
+  number={1},
+  pages={65--98},
+  year={2017},
+  publisher={SIAM},
+  eprint={1411.1607},
+  eprinttype={arxiv},
+  eprintclass={cs.MS},
+  doi={10.1137/141000671}
+}
+
+@article{christ2023plots,
+  author={Christ, Simon and Schwabeneder, Daniel and Rackauckas, Christopher
+          and Borregaard, Michael Krabbe and Breloff, Thomas},
+  title={Plots.jl --- a user extendable plotting {API} for the {J}ulia
+         programming language},
+  journal={Journal of Open Research Software},
+  volume={11},
+  number={1},
+  pages={5},
+  year={2023},
+  doi={10.5334/jors.431},
+  eprint={2204.08775},
+  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}
+}