Package detestset: testset for initial value problems of differential equations in R

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1 Package detestset: testset for initial value problems of differential equations in R Karline Soetaert Jeff Cash CEME Department of mathematics Netherlands Institute of Ecology Imperial College London The Netherlands U.K. Francesca Mazzia Diparnto di Matematica Universita di Bari Italy Abstract R package detestset contains the R-version of the ODE and DAE initial value problems test set from If the model problem is small enough, then it is implemented in pure R. For larger models, the problem specified in FORTRAN code at the website of Jeff Cash ma.ic.ac.uk/~jcash/ivp_software were used. These implementations were compiled as DLLs, and included in the package. The code of these models can be found in the packages inst/examples/dynload subdirectory. For a number of small models, we show how to implement them in R. Keywords: ordinary differential equations, differential algebraic equations, initial value problems, testset, R. > out <- andrews() > mtext(outer = TRUE, side = 3, line = -1.5, "andrews", cex = 1.5)

2 2 Package detestset: testset for initial value problems of differential equations in R q1 andrews q2 q q4 q5 q q7 dq1 dq Figure 1: the andrews problem- see text for R-code

3 Karline Soetaert, Jeff Cash and Francesca Mazzia 3 1 beam Figure 2: Solution of beam - see text for R-code > out <- beam() > mtext(outer = TRUE, side = 3, line = -1.5, "beam", cex = 1.5)

4 4 Package detestset: testset for initial value problems of differential equations in R xl caraxis yl xr yr xla yla xra yra lam Figure 3: Solution of caraxis - see text for R-code > out <- caraxis() > mtext(outer = TRUE, side = 3, line = -1.5, "caraxis", cex = 1.5)

5 Karline Soetaert, Jeff Cash and Francesca Mazzia 5 phi1 crank phi2 x q1 q2 q e 05 2e e 06 5e q4 vphi1 vphi2 1.0e e Figure 4: Solution of crank - see text for R-code > out <- crank() > mtext(outer = TRUE, side = 3, line = -1.5, "crank", cex = 1.5)

6 6 Package detestset: testset for initial value problems of differential equations in R 1 E5 2 1e 18 1e 10 1e 05 1e+03 1e+11 1e 20 1e 14 1e 05 1e+03 1e e 20 1e 16 1e 12 1e 05 1e+03 1e+11 1e 30 1e 20 1e 10 1e 05 1e+03 1e+11 Figure 5: Solution of E5 - see text for R-code > out <- E5() > plot(out, lwd = 2, ask = FALSE, log = "xy") > mtext(outer = TRUE, side = 3, line = -1.5, "E5", cex = 1.5)

7 Karline Soetaert, Jeff Cash and Francesca Mazzia 7 NO emep NO2 SO2 0.0e e+10 0e+00 2e+05 4e+05 1e+10 5e+10 0e+00 2e+05 4e e e+11 0e+00 2e+05 4e+05 4e+12 1e+13 CO 0e+00 2e+05 4e e e+13 CH4 0e+00 2e+05 4e+05 0e+00 6e+10 C2H6 0e+00 2e+05 4e+05 NC4H10 C2H4 C3H6 0e+00 8e+10 0e+00 2e+05 4e+05 0e+00 6e+09 0e+00 2e+05 4e+05 0e+00 3e+09 0e+00 2e+05 4e+05 Figure 6: Solution of emep - see text for R-code > out <- emep() > mtext(outer = TRUE, side = 3, line = -1.5, "emep", cex = 1.5)

8 8 Package detestset: testset for initial value problems of differential equations in R px1 fekete px2 px px4 px5 px px7 px8 px Figure 7: Solution of fekete - see text for R-code > out <- fekete() > mtext(outer = TRUE, side = 3, line = -1.5, "fekete", cex = 1.5)

9 Karline Soetaert, Jeff Cash and Francesca Mazzia 9 Pr hires Pfr PrX PfrX PrX2 PfrX PfrX2E E Figure 8: Solution of hires - see text for R-code > out <- hires() > plot(out, lwd = 2, ask = FALSE) > mtext(outer = TRUE, side = 3, line = -1.5, "hires", cex = 1.5)

10 10 Package detestset: testset for initial value problems of differential equations in R 1 nand Figure 9: Solution of nand - see text for R-code The nand problem is most efficiently solved with daspk > out <- nand(method = daspk) > mtext(outer = TRUE, side = 3, line = -1.5, "nand", cex = 1.5)

11 Karline Soetaert, Jeff Cash and Francesca Mazzia 11 1 orego e 01 1e+01 1e Figure 10: Solution of orego - see text for R-code > out <- orego() > plot(out, lwd = 2, ask = FALSE, log = "y") > mtext(outer = TRUE, side = 3, line = -1.5, "orego", cex = 1.5)

12 12 Package detestset: testset for initial value problems of differential equations in R NO2 pollution NO O3P e e 09 O3 HO2 OH e e 07 0e+00 3e 07 HCHO CO ALD Figure 11: Solution of pollution - see text for R-code > out <- pollution() > mtext(outer = TRUE, side = 3, line = -1.5, "pollution", cex = 1.5)

13 Karline Soetaert, Jeff Cash and Francesca Mazzia 13 1 ring e+00 4e 04 8e 04 0e+00 4e 04 8e 04 0e+00 4e 04 8e e+00 4e 04 8e 04 0e+00 4e 04 8e 04 0e+00 4e 04 8e e+00 4e 04 8e e e 06 0e+00 4e 04 8e 04 2e 06 1e 06 0e+00 4e 04 8e 04 Figure 12: Solution of ring - see text for R-code > out <- ring() > mtext(outer = TRUE, side = 3, line = -1.5, "ring", cex = 1.5)

14 14 Package detestset: testset for initial value problems of differential equations in R 1 rober e 05 1e+03 1e+11 0e+00 2e 05 1e 05 1e+03 1e e 05 1e+03 1e+11 Figure 13: Solution of rober - see text for R-code > out <- rober() > plot(out, lwd = 2, ask = FALSE, log = "x") > mtext(outer = TRUE, side = 3, line = -1.5, "rober", cex = 1.5)

15 Karline Soetaert, Jeff Cash and Francesca Mazzia 15 1 transistor Figure 14: Solution of transistor - see text for R-code > out <- transistor() > plot(out, lwd = 2, ask = FALSE) > mtext(outer = TRUE, side = 3, line = -1.5, "transistor", cex = 1.5)

16 16 Package detestset: testset for initial value problems of differential equations in R phi1.2 tube phi2.3 phi e+00 8e phi3.4 phi3.5 phi e+00 6e e+00 6e phi5.10 phi6.5 phi e+00 8e e+00 6e Figure 15: Solution of tube - see text for R-code > out <- tube() > mtext(outer = TRUE, side = 3, line = -1.5, "tube", cex = 1.5)

17 Karline Soetaert, Jeff Cash and Francesca Mazzia 17 y1 twobit y2 y y4 y5 y y7 y8 y Figure 16: Solution of twobit - see text for R-code > out <- twobit() > mtext(outer = TRUE, side = 3, line = -1.5, "twobit", cex = 1.5)

18 18 Package detestset: testset for initial value problems of differential equations in R y1 vdpol y Figure 17: Solution of vdpol - see text for R-code > out <- vdpol() > plot(out, lwd = 2, ask = FALSE) > mtext(outer = TRUE, side = 3, line = -1.5, "vdpol", cex = 1.5)

19 Karline Soetaert, Jeff Cash and Francesca Mazzia 19 x wheelset y z e e 05 1e 04 0e+00 1e 04 theta phi v Figure 18: Solution of wheelset an implicit differential equation model - index 2, dimension 17 - see text for R-code > out <- wheelset() > plot(out, which = 1:6, lwd = 2, ask = FALSE) > mtext(outer = TRUE, side = 3, line = -1.5, "wheelset", cex = 1.5)

20 20 Package detestset: testset for initial value problems of differential equations in R 1. References F. Mazzia and C. Magherini. Test Set for Initial Value Problem Solvers, release 2.4. Department of Mathematics, University of Bari and INdAM, Research Unit of Bari, February Available at testset. Karline Soetaert, Thomas Petzoldt and R. Woodrow Setzer (2009). 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). R package version 1.7. Karline Soetaert (2009). rootsolve: Nonlinear root finding, equilibrium and steady-state analysis of ordinary differential equations. R-package version 1.6 Affiliation: Karline Soetaert Centre for Estuarine and Marine Ecology (CEME) Netherlands Institute of Ecology (NIOO) 4401 NT Yerseke, Netherlands k.soetaert@nioo.knaw.nl URL: Jeff Cash Imperial College London South Kensington Campus London SW7 2AZ, U.K. j.cash@imperial.ac.uk URL: Francesca Mazzia Diparnto di Matematica Universita di Bari Via Orabona 4, BARI Italy mazzia@dm.uniba.it URL:

Solving partial differential equations, using R package ReacTran

Solving partial differential equations, using R package ReacTran Karline Soetaert and Filip Meysman Centre for Estuarine and Marine Ecology Netherlands Institute of Ecology The Netherlands Abstract R -package