additional references

Author: SKopecz

paper/paper.bib

@@ -11,3 +11,160 @@ @article{bartel2024structure
   eprinttype={arxiv},
   eprintclass={math.NA}
 }
+
+@article{burchard2003,
+title = {A high-order conservative Patankar-type discretisation for stiff systems of production–destruction equations},
+journal = {Applied Numerical Mathematics},
+volume = {47},
+number = {1},
+pages = {1-30},
+year = {2003},
+issn = {0168-9274},
+doi = {https://doi.org/10.1016/S0168-9274(03)00101-6},
+url = {https://www.sciencedirect.com/science/article/pii/S0168927403001016},
+author = {Hans Burchard and Eric Deleersnijder and Andreas Meister},
+keywords = {Patankar-type schemes, Runge–Kutta methods, Unconditional positivity, Conservativity},
+}
+
+article{kopeczmeister2018order2,
+title = {On order conditions for modified Patankar–Runge–Kutta schemes},
+journal = {Applied Numerical Mathematics},
+volume = {123},
+pages = {159-179},
+year = {2018},
+issn = {0168-9274},
+doi = {https://doi.org/10.1016/j.apnum.2017.09.004},
+url = {https://www.sciencedirect.com/science/article/pii/S0168927417301861},
+author = {S. Kopecz and A. Meister},
+keywords = {Patankar-type schemes, Runge–Kutta methods, Unconditional positivity, Conservativity},
+}
+
+@article {kopeczmeister2018order3,
+    AUTHOR = {Kopecz, Stefan and Meister, Andreas},
+     TITLE = {Unconditionally positive and conservative third order modified
+              {P}atankar-{R}unge-{K}utta discretizations of
+              production-destruction systems},
+   JOURNAL = {BIT},
+  FJOURNAL = {BIT. Numerical Mathematics},
+    VOLUME = {58},
+      YEAR = {2018},
+    NUMBER = {3},
+     PAGES = {691--728},
+      ISSN = {0006-3835,1572-9125},
+   MRCLASS = {65L06 (65L05 65L20)},
+  MRNUMBER = {3855688},
+MRREVIEWER = {Luigi\ Brugnano},
+       DOI = {10.1007/s10543-018-0705-1},
+       URL = {https://doi.org/10.1007/s10543-018-0705-1},
+}
+
+@article {kopeczmeister2019,
+    AUTHOR = {Kopecz, Stefan and Meister, Andreas},
+     TITLE = {On the existence of three-stage third-order modified
+              {P}atankar-{R}unge-{K}utta schemes},
+   JOURNAL = {Numer. Algorithms},
+  FJOURNAL = {Numerical Algorithms},
+    VOLUME = {81},
+      YEAR = {2019},
+    NUMBER = {4},
+     PAGES = {1473--1484},
+      ISSN = {1017-1398,1572-9265},
+   MRCLASS = {65L06},
+  MRNUMBER = {3987250},
+       DOI = {10.1007/s11075-019-00680-3},
+       URL = {https://doi.org/10.1007/s11075-019-00680-3},
+}
+
+@article {izgin2022stability1,
+    AUTHOR = {Izgin, Thomas and Kopecz, Stefan and Meister, Andreas},
+     TITLE = {On {L}yapunov stability of positive and conservative time
+              integrators and application to second order modified
+              {P}atankar-{R}unge-{K}utta schemes},
+   JOURNAL = {ESAIM Math. Model. Numer. Anal.},
+  FJOURNAL = {ESAIM. Mathematical Modelling and Numerical Analysis},
+    VOLUME = {56},
+      YEAR = {2022},
+    NUMBER = {3},
+     PAGES = {1053--1080},
+      ISSN = {2822-7840,2804-7214},
+   MRCLASS = {65L05 (65L06 65L20)},
+  MRNUMBER = {4420893},
+MRREVIEWER = {Qin\ Sheng},
+       DOI = {10.1051/m2an/2022031},
+       URL = {https://doi.org/10.1051/m2an/2022031},
+}
+
+@article {izgin2022stability2,
+    AUTHOR = {Izgin, Thomas and Kopecz, Stefan and Meister, Andreas},
+     TITLE = {On the stability of unconditionally positive and linear
+              invariants preserving time integration schemes},
+   JOURNAL = {SIAM J. Numer. Anal.},
+  FJOURNAL = {SIAM Journal on Numerical Analysis},
+    VOLUME = {60},
+      YEAR = {2022},
+    NUMBER = {6},
+     PAGES = {3029--3051},
+      ISSN = {0036-1429,1095-7170},
+   MRCLASS = {65L05 (34D20 65L20)},
+  MRNUMBER = {4509959},
+MRREVIEWER = {Lajos\ L\'oczi},
+       DOI = {10.1137/22M1480318},
+       URL = {https://doi.org/10.1137/22M1480318},
+}
+
+@article {huang2023,
+    AUTHOR = {Huang, Juntao and Izgin, Thomas and Kopecz, Stefan and
+              Meister, Andreas and Shu, Chi-Wang},
+     TITLE = {On the stability of strong-stability-preserving modified
+              {P}atankar-{R}unge-{K}utta schemes},
+   JOURNAL = {ESAIM Math. Model. Numer. Anal.},
+  FJOURNAL = {ESAIM. Mathematical Modelling and Numerical Analysis},
+    VOLUME = {57},
+      YEAR = {2023},
+    NUMBER = {2},
+     PAGES = {1063--1086},
+      ISSN = {2822-7840,2804-7214},
+   MRCLASS = {65L05 (65L06 65L20)},
+  MRNUMBER = {4574004},
+MRREVIEWER = {Raymond\ J.\ Spiteri},
+       DOI = {10.1051/m2an/2023005},
+       URL = {https://doi.org/10.1051/m2an/2023005},
+}
+
+
+@article {huang2019order3,
+    AUTHOR = {Huang, Juntao and Zhao, Weifeng and Shu, Chi-Wang},
+     TITLE = {A third-order unconditionally positivity-preserving scheme for
+              production-destruction equations with applications to
+              non-equilibrium flows},
+   JOURNAL = {J. Sci. Comput.},
+  FJOURNAL = {Journal of Scientific Computing},
+    VOLUME = {79},
+      YEAR = {2019},
+    NUMBER = {2},
+     PAGES = {1015--1056},
+      ISSN = {0885-7474,1573-7691},
+   MRCLASS = {65M06 (76Nxx 76V05)},
+  MRNUMBER = {3969000},
+       DOI = {10.1007/s10915-018-0881-9},
+       URL = {https://doi.org/10.1007/s10915-018-0881-9},
+}
+
+@article {huang2019order2,
+    AUTHOR = {Huang, Juntao and Shu, Chi-Wang},
+     TITLE = {Positivity-preserving time discretizations for
+              production-destruction equations with applications to
+              non-equilibrium flows},
+   JOURNAL = {J. Sci. Comput.},
+  FJOURNAL = {Journal of Scientific Computing},
+    VOLUME = {78},
+      YEAR = {2019},
+    NUMBER = {3},
+     PAGES = {1811--1839},
+      ISSN = {0885-7474,1573-7691},
+   MRCLASS = {65M06 (65L06 65M20 76V05)},
+  MRNUMBER = {3934688},
+MRREVIEWER = {Qifeng\ Zhang},
+       DOI = {10.1007/s10915-018-0852-1},
+       URL = {https://doi.org/10.1007/s10915-018-0852-1},
+}