The following bibliography may serve as a starting point for further reading. It can be downloaded as bibtex .bib-file.

Package documentation

References of the original algorithms

Please consult the original publications for gaining full understanding of the algorithms.

Papers citing deSolve

Bibliography

1. Soetaert K, Petzoldt T, Setzer RW. deSolve: General solvers for initial value problems of ordinary differential equations (oDE), partial differential equations (pDE), differential algebraic equations (dAE) and delay differential equations (dDE) [Internet]. 2016. Available: http://cran.r-project.org/web/packages/deSolve/deSolve.pdf

2. Soetaert K, Petzoldt T, Setzer RW. R package deSolve: Solving initial value differential equations in r [Internet]. 2016. Available: http://cran.r-project.org/web/packages/deSolve/vignettes/deSolve.pdf

3. Soetart K, Petzoldt T, Setzer RW. R package deSolve: Writing code in compiled languages [Internet]. 2016. Available: http://cran.r-project.org/web/packages/deSolve/vignettes/compiledCode.pdf

4. Soetaert K, Petzoldt T, Setzer RW. Solving differential equations in r: Package deSolve. Journal of Statistical Software. 2010;33: 1–25. doi:10.18637/jss.v033.i09

5. Soetaert K, Petzoldt T. Inverse modelling, sensitivity and Monte Carlo analysis in R using package FME. Journal of Statistical Software. 2010;33: 1–28. doi:10.18637/jss.v033.i03

6. Soetaert K, Petzoldt T, Setzer RW. Solving differential equations in R. The R Journal. 2010;2: 5–15. Available: http://journal.r-project.org/archive/2010-2/RJournal_2010-2_Soetaert~et~al.pdf

7. Soetaert K, Herman PMJ. A practical guide to ecological modelling using r as a simulation platform [Internet]. Springer; 2009. pp. 1–372. Available: http://www.springer.com/life+sci/ecology/book/978-1-4020-8623-6

8. Soetaert K, Cash J, Mazzia F. Solving differential equations in r [Internet]. Springer; 2012. Available: http://www.springer.com/statistics/computational+statistics/book/978-3-642-28069-6

9. Soetaert K. Mathematical modelling of the environment - are there enough data? 2009.

10. Petzoldt T. Dynamic simulation models - is r powerful enough? 2009.

11. Petzoldt T. Swimming in clear lakes: How model coupling with r helps to improve water quality. 2014.

12. Petzoldt T, Soetaert K. Using r for systems understanding - a dynamic approach [Internet]. 2011. Available: slides/petz_soet2011.pdf

13. Soetaert M K., Petzoldt T. Solving differential equations in r. 2010. doi:10.1063/1.3498463

14. Soetaert K, Petzoldt T. Simulating differential equation models in r – pre-conference tutorial [Internet]. 2011. Available: slides/tutorial.pdf

15. Soetaert K. Solving differential equations in r (plenary talk). 2014.

16. Soetaert K, Petzoldt T. Simulating differential equation models in r – pre-conference tutorial [Internet]. 2014. Available: user2014/tutorial.pdf

17. Soetaert K, Meysman F, Petzoldt T. Solving differential equations in r. In: Simos TE, Psihoyios G, Tsitouras C, editors. AIP conference proceedings. AIP; 2010. pp. 31–34. doi:10.1063/1.3498463

18. Setzer RW. The odesolve package: Solvers for ordinary differential equations. 2001.

19. Mazzia F, Cash JR, Soetaert K. Solving boundary value problems in the open source software r: Package bvpSolve. Opuscula mathematica. 2014;34: 387–403. doi:10.7494/OpMath.2014.34.2.387

20. Soetaert K, Meysman F. Reactive transport in aquatic ecosystems: Rapid model prototyping in the open source software R. Environmental Modelling and Software. 2012;32: 49–60. doi:10.1016/j.envsoft.2011.08.011

21. Soetaert K, Meysman F. ReacTran: Reactive transport modelling in 1D, 2D and 3D. 2010.

22. Ellner SP, Guckenheimer J. Dynamic models in biology [Internet]. Princeton University Press; 2006. pp. 1–329. Available: http://www.cam.cornell.edu/~dmb/DMBsupplements.html

23. Stevens MH. A primer of ecology with r [Internet]. Springer; 2009. pp. 1–401. Available: http://www.springer.com/us/book/9780387898810

24. Kutta W. Beitrag zur näherungweisen Integration totaler Differentialgleichungen. Z Math Phys. 1901;46: 435–453.

25. Fehlberg E. Klassische Runge-Kutta-Formeln fuenfter and siebenter Ordnung mit Schrittweiten-Kontrolle. Computing (Arch Elektron Rechnen). 1967;4: 93–106.

26. Dormand JR, Prince PJ. A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics. 1980;6: 19–26.

27. Prince PJ, Dormand JR. High order embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics. 1981;7: 67–75.

28. Butcher JC. The numerical analysis of ordinary differential equations, Runge-Kutta and general linear methods. Chichester; New York.: John Wiley & Sons; 1987. pp. 1–9.

29. Bogacki P, Shampine LF. A 3(2) pair of Runge-Kutta formulas. Applied Mathematics Letters. 1989;2: 1–9.

30. Cash JR, Karp AH. A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software. 1990;16: 201–222.

31. Engeln-Muellges G, Reutter F. Numerik algorithmen: Entscheidungshilfe zur auswahl und nutzung. Duesseldorf: VDI Verlag; 1996.

32. Press WH, Teukolsky SA, Vetterling WT, Flannery BP. Numerical recipes in C. 3rd ed. Cambridge University Press; 2007.

33. Hindmarsh AC. ODEPACK, a systematized collection of ODE solvers. In: Stepleman R, editor. Scientific computing applications of mathematics and computing to the physical sciences. Amsterdam: IMACS / North-Holland; 1983. pp. 55–64.

34. Petzold LR. A description of DASSL: A differential/algebraic system solver. In: Stepleman RA, editor. Scientific computing applications of mathematics and computing to the physical sciences. Amsterdam: IMACS / North-Holland; 1983. pp. 65–68.

35. Petzold LR. Automatic selection of methods for solving stiff and nonstiff systems of ordinary differential equations. SIAM Journal on Scientific and Statistical Computing. 1983;4: 136–148.

36. Brown PN, Byrne GD, Hindmarsh AC. VODE, a variable-coefficient oDE solver. SIAM J Sci Stat Comput. 1989;10: 1038–1051.

37. Brown PN, Hindmarsh AC. Reduced storage matrix methods in stiff oDE systems. Applied Mathematics and Computation. Elsevier; 1989;31: 40–91.

38. Brown PN, Hindmarsh AC, Petzold LR. Using Krylov methods in the solution of large-scale differential-algebraic systems. SIAM J Sci Comput. Philadelphia, PA, USA: Society for Industrial; Applied Mathematics; 1994;15: 1467–1488. doi:10.1137/0915088

39. Brenan KE, Campbell SL, Petzold LR. Numerical solution of initial-value problems in differential-algebraic equations. SIAM Classics in Applied Mathematics; 1996.

40. Brown PN, Hindmarsh AC, Petzold LR. Consistent initial condition calculation for differential-algebraic systems. SIAM Journal on Scientific Computing. SIAM; 1998;19: 1495–1512.

41. Hairer E, Norsett SP, Wanner G. Solving ordinary differential equations i: Nonstiff problems. second revised edition. Heidelberg: Springer-Verlag; 2009.

42. Hairer E, Wanner G. Solving ordinary differential equations iI: Stiff and differential-algebraic problems. second revised edition. Heidelberg: Springer-Verlag; 2010.