The following bibliography may serve as a starting point for further reading. It can be downloaded as bibtex .bib-file.
Manuals: [1], [2], [3]
Papers: [4], [5], [6]
Books: [7], [8]
Conferences: [9], [10], [11], [12], [13], [14], [15], [16], [17]
Papers about related software: [18], [19], [20], [21]
Some books from other authors: [22],[23]
Runge-Kutta algorithms: [24], [25], [26], [27], [28], [29], [30], [31], [32]
ODEPACK algorithms: [33], [34], [35], [36], [37], [38], [39], [40], [41], [42]
Please consult the original publications for gaining full understanding of the algorithms.
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.