Hello all,

I ran the example system given in section 17.7 and the results are shown below. Did anyone else do this and obtain the same results?

The results shown below only go up to x=1.010439. The total results for x = 0 to x = 15 are shown in the attached file.

Also attached is my first use of PSplot outside of the example. (Anyone who read my threads on PSplot knows that I should be proud of this. LOL)

Lotka - Volterra Problem (17.7.2) Through Direct Integration of the Equations

Using StepperSie with output(-1) the following results were obtained

Number of good steps 310 The number of bad steps 295

================================================== ===============

xsave[i] ysave[0][i] ysave[1][i] ysave[2][i]

0.000000 150.000000 10.000000 10.000000
0.000001 149.999985 10.000005 10.000000
0.000008 149.999881 10.000040 10.000000
0.000056 149.999155 10.000282 10.000000
0.000393 149.994103 10.001965 10.000000
0.001221 149.981687 10.006104 10.000004
0.002630 149.960529 10.013154 10.000017
0.004674 149.929818 10.023383 10.000055
0.007311 149.890179 10.036580 10.000134
0.010502 149.842145 10.052562 10.000276
0.014204 149.786340 10.071116 10.000505
0.018379 149.723301 10.092058 10.000846
0.022995 149.653490 10.115226 10.001324
0.028023 149.577298 10.140484 10.001967
0.033440 149.495056 10.167715 10.002802
0.039221 149.407075 10.196807 10.003856
0.044362 149.328681 10.222695 10.004935
0.049502 149.250128 10.248600 10.006147
0.056844 149.137676 10.285626 10.008109
0.064185 149.024904 10.322683 10.010344
0.072148 148.902211 10.362916 10.013077
0.080112 148.779143 10.403179 10.016132
0.088721 148.645664 10.446740 10.019797
0.097331 148.511747 10.490329 10.023840
0.106540 148.368030 10.536974 10.028582
0.115749 148.223815 10.583638 10.033758
0.125518 148.070279 10.633156 10.039724
0.135288 147.916185 10.682681 10.046179
0.145583 147.753193 10.734871 10.053512
0.155879 147.589587 10.787051 10.061392
0.166669 147.417463 10.841716 10.070237
0.177460 147.244672 10.896347 10.079685
0.188716 147.063714 10.953290 10.090183
0.199972 146.882038 11.010171 10.101340
0.211667 146.692528 11.069189 10.113629
0.223361 146.502251 11.128111 10.126632
0.235469 146.304458 11.188997 10.140847
0.247576 146.105856 11.249747 10.155829
0.260072 145.900047 11.312283 10.172099
0.272567 145.693391 11.374637 10.189190
0.285427 145.479835 11.438597 10.207638
0.298287 145.265398 11.502321 10.226958
0.311488 145.044364 11.567467 10.247702
0.324689 144.822423 11.632317 10.269369
0.338210 144.594185 11.698402 10.292519
0.351730 144.365020 11.764123 10.316640
0.365549 144.129858 11.830888 10.342298
0.379368 143.893755 11.897215 10.368973
0.393464 143.651952 11.964392 10.397234
0.407561 143.409202 12.031049 10.426556
0.421916 143.161044 12.098361 10.457506
0.436271 142.911940 12.165065 10.489557
0.450867 142.657714 12.232228 10.523274
0.465463 142.402551 12.298688 10.558129
0.480282 142.142546 12.365410 10.594681
0.495101 141.881620 12.431329 10.632404
0.510128 141.616120 12.497313 10.671852
0.525155 141.349725 12.562389 10.712501
0.540376 141.079014 12.627334 10.754895
0.555596 140.807441 12.691260 10.798516
0.570997 140.531800 12.754862 10.843899
0.586398 140.255337 12.817330 10.890531
0.601968 139.975043 12.879281 10.938936
0.617538 139.693976 12.939978 10.988605
0.633265 139.409308 12.999969 11.040056
0.648993 139.123922 13.058583 11.092782
0.664869 138.835158 13.116303 11.147289
0.680744 138.545740 13.172520 11.203077
0.696759 138.253163 13.227657 11.260642
0.712774 137.960005 13.281163 11.319487
0.728919 137.663910 13.333405 11.380095
0.745065 137.367312 13.383888 11.441976
0.761332 137.068008 13.432923 11.505596
0.777600 136.768287 13.480072 11.570475
0.793981 136.466106 13.525593 11.637059
0.810361 136.163600 13.569103 11.704880
0.826846 135.858900 13.610807 11.774356
0.843330 135.553974 13.650376 11.845038
0.859908 135.247149 13.687969 11.917310
0.876485 134.940203 13.723310 11.990748
0.893144 134.631686 13.756509 12.065691
0.909803 134.323158 13.787347 12.141749
0.926529 134.013424 13.815890 12.219206
0.943256 133.703794 13.841970 12.297718
0.960034 133.393362 13.865617 12.377498
0.976813 133.083151 13.886711 12.458263
0.993626 132.772577 13.905254 12.540143
1.010439 132.462344 13.921168 12.622926

Thanks
Matt

Idiot Disclaimer

"I am an engineer not a highly trained programmer. Please be gentle"

...
I ran the example system given in section 17.7
Hmmm...
I reached pretty much the same final values with 24 steps. With Visual C++ 2008 Express, here's my complete output:


Settings in main()
rtol = 1.000000e-007
atol = 1.000000e-011
h1 = 1.000000e-006
hmin = 0.000000e+000
x1 = 0.000000e+000
x2 = 1.500000e+001


Number of successful steps: 24
Number of bad steps: 0
Number of function evaluations: 1121

Number of stored intermediate values: 25

xsave[i] ysave[0][i] ysave[1][i] ysave[2][i]
================================================== ========
0.000000e+000 1.500000e+002 1.000000e+001 1.000000e+001
1.000000e-006 1.500000e+002 1.000001e+001 1.000000e+001
7.957011e-006 1.499999e+002 1.000004e+001 1.000000e+001
5.635701e-005 1.499992e+002 1.000028e+001 1.000000e+001
3.930763e-004 1.499941e+002 1.000197e+001 1.000000e+001
1.220583e-003 1.499817e+002 1.000610e+001 1.000000e+001
3.334776e-003 1.499499e+002 1.001668e+001 1.000003e+001
7.794864e-003 1.498829e+002 1.003900e+001 1.000015e+001
1.933128e-002 1.497089e+002 1.009684e+001 1.000094e+001
6.346953e-002 1.490359e+002 1.031907e+001 1.001011e+001
2.022527e-001 1.468451e+002 1.102169e+001 1.010368e+001
3.794262e-001 1.438928e+002 1.189749e+001 1.036909e+001
7.530265e-001 1.372209e+002 1.340812e+001 1.147295e+001
1.511343e+000 1.236556e+002 1.315542e+001 1.521972e+001
2.351849e+000 1.126547e+002 8.887676e+000 1.667338e+001
3.223659e+000 1.057336e+002 6.138250e+000 1.314520e+001
4.238799e+000 9.968974e+001 5.858115e+000 8.580669e+000
5.496154e+000 9.149635e+001 8.199620e+000 5.753410e+000
7.124291e+000 7.691227e+001 1.286201e+001 6.410853e+000
8.669488e+000 6.335021e+001 1.082086e+001 9.513077e+000
9.860410e+000 5.696533e+001 7.341238e+000 8.365361e+000
1.107571e+001 5.259727e+001 6.153467e+000 5.510094e+000
1.257458e+001 4.779032e+001 6.943049e+000 3.209536e+000
1.457335e+001 4.043690e+001 9.997342e+000 2.312113e+000
1.500000e+001 3.868822e+001 1.071852e+001 2.348051e+000


Also attached is my first use of PSplot outside of the example.

Hmmmm.... (again)

It looks like the foxes are on the way down and the rabbits are rising, but grass futures don't look very good right now. Is this a metaphor for the current state of affairs, or what?

Regards,

Dave

It looks like the foxes are on the way down and the rabbits are rising, but grass futures don't look very good right now.

Yeah you could deduce that from my graph.

Thanks for the verification.

Matt