| Variable ▲ | Initial | Minimal | Maximal | Final Value | |
|---|---|---|---|---|---|
| 1 | B | 0.05 | 0.05 | 6.717 | 6.7166667 |
| 2 | S | 5 | -1.494e-24 | 5 | -9.427991e-31 |
| 3 | t | 0 | 0 | 20 | 20 |
Calculated values
Data Table (134 records)
| # | t | S | B |
|---|---|---|---|
| 1 | 0 | 5 | 0.05 |
| 2 | 0.1625 | 4.9981265 | 0.05249789 |
| 3 | 0.26375 | 4.9969125 | 0.05411698 |
| 4 | 0.415625 | 4.9950204 | 0.05663972 |
| 5 | 0.6434375 | 4.9920154 | 0.060646035 |
| 6 | 0.87721014 | 4.988711 | 0.06505194 |
| 7 | 1.1068099 | 4.985232 | 0.06969064 |
| 8 | 1.3325653 | 4.9815693 | 0.07457405 |
| 9 | 1.5545992 | 4.977717 | 0.07971062 |
| 10 | 1.7730314 | 4.973668 | 0.085108966 |
| 11 | 1.9879763 | 4.9694166 | 0.090777904 |
| 12 | 2.199543 | 4.9649553 | 0.09672636 |
| 13 | 2.4078352 | 4.9602776 | 0.1029634 |
| 14 | 2.6129527 | 4.955376 | 0.10949828 |
| 15 | 2.8149898 | 4.950245 | 0.11634035 |
| 16 | 3.0140376 | 4.9448757 | 0.12349915 |
| 17 | 3.2101824 | 4.939262 | 0.13098434 |
| 18 | 3.403508 | 4.933396 | 0.13880573 |
| 19 | 3.594093 | 4.92727 | 0.1469733 |
| 20 | 3.7820144 | 4.920877 | 0.15549713 |
| 21 | 3.9673448 | 4.9142094 | 0.1643875 |
| 22 | 4.1501546 | 4.907259 | 0.1736548 |
| 23 | 4.330511 | 4.9000177 | 0.18330956 |
| 24 | 4.5084786 | 4.892478 | 0.1933625 |
| 25 | 4.68412 | 4.8846316 | 0.20382445 |
| 26 | 4.857495 | 4.87647 | 0.21470639 |
| 27 | 5.0286603 | 4.8679852 | 0.22601946 |
| 28 | 5.197672 | 4.859169 | 0.23777494 |
| 29 | 5.3645835 | 4.850012 | 0.24998426 |
| 30 | 5.5294456 | 4.8405056 | 0.262659 |
| 31 | 5.692308 | 4.8306417 | 0.27581087 |
| 32 | 5.8532186 | 4.820411 | 0.28945172 |
| 33 | 6.0122232 | 4.809805 | 0.3035936 |
| 34 | 6.169367 | 4.7988133 | 0.31824866 |
| 35 | 6.324692 | 4.787428 | 0.3334292 |
| 36 | 6.47824 | 4.775639 | 0.34914765 |
| 37 | 6.630051 | 4.7634373 | 0.36541665 |
| 38 | 6.780164 | 4.7508135 | 0.38224894 |
| 39 | 6.928616 | 4.7377567 | 0.39965743 |
| 40 | 7.0754437 | 4.724259 | 0.4176551 |
| 41 | 7.2206817 | 4.7103086 | 0.4362552 |
| 42 | 7.364364 | 4.6958966 | 0.455471 |
| 43 | 7.506524 | 4.681013 | 0.47531608 |
| 44 | 7.6471925 | 4.665647 | 0.49580398 |
| 45 | 7.7864017 | 4.6497884 | 0.5169485 |
| 46 | 7.92418 | 4.633427 | 0.53876364 |
| 47 | 8.060557 | 4.6165524 | 0.5612633 |
| 48 | 8.195562 | 4.5991535 | 0.5844618 |
| 49 | 8.329221 | 4.5812197 | 0.6083735 |
| 50 | 8.46156 | 4.5627403 | 0.63301295 |
| 51 | 8.592607 | 4.543704 | 0.65839475 |
| 52 | 8.7223835 | 4.5241 | 0.6845337 |
| 53 | 8.850917 | 4.5039163 | 0.7114448 |
| 54 | 8.9782295 | 4.483143 | 0.7391431 |
| 55 | 9.104343 | 4.461767 | 0.7676438 |
| 56 | 9.229282 | 4.4397783 | 0.7969624 |
| 57 | 9.353067 | 4.4171643 | 0.8271144 |
| 58 | 9.475719 | 4.3939133 | 0.85811543 |
| 59 | 9.5972595 | 4.370014 | 0.8899814 |
| 60 | 9.717707 | 4.3454537 | 0.9227282 |
| 61 | 9.837081 | 4.320221 | 0.956372 |
| 62 | 9.955401 | 4.294303 | 0.9909291 |
| 63 | 10.072685 | 4.2676883 | 1.026416 |
| 64 | 10.188951 | 4.240363 | 1.0628489 |
| 65 | 10.304218 | 4.2123165 | 1.100245 |
| 66 | 10.418501 | 4.183534 | 1.1386209 |
| 67 | 10.531817 | 4.154005 | 1.1779935 |
| 68 | 10.644183 | 4.123715 | 1.2183803 |
| 69 | 10.755614 | 4.0926514 | 1.2597984 |
| 70 | 10.866126 | 4.060801 | 1.302265 |
| 71 | 10.975733 | 4.0281515 | 1.3457981 |
| 72 | 11.084451 | 3.9946885 | 1.3904154 |
| 73 | 11.192293 | 3.9603992 | 1.4361346 |
| 74 | 11.299273 | 3.9252696 | 1.4829738 |
| 75 | 11.405406 | 3.8892865 | 1.5309513 |
| 76 | 11.510704 | 3.8524363 | 1.580085 |
| 77 | 11.615181 | 3.8147044 | 1.630394 |
| 78 | 11.718849 | 3.7760775 | 1.6818966 |
| 79 | 11.82172 | 3.7365415 | 1.7346115 |
| 80 | 11.923808 | 3.6960816 | 1.7885578 |
| 81 | 12.025123 | 3.654684 | 1.8437544 |
| 82 | 12.125676 | 3.6123345 | 1.9002208 |
| 83 | 12.22548 | 3.569018 | 1.957976 |
| 84 | 12.324546 | 3.5247202 | 2.0170398 |
| 85 | 12.520504 | 3.4331217 | 2.1391711 |
| 86 | 12.617417 | 3.385791 | 2.2022786 |
| 87 | 12.713635 | 3.3374195 | 2.2667742 |
| 88 | 12.809166 | 3.2879915 | 2.3326778 |
| 89 | 12.904019 | 3.2374923 | 2.4000103 |
| 90 | 12.998205 | 3.1859062 | 2.4687917 |
| 91 | 13.091734 | 3.1332176 | 2.5390432 |
| 92 | 13.184612 | 3.0794113 | 2.610785 |
| 93 | 13.276852 | 3.024471 | 2.6840386 |
| 94 | 13.368459 | 2.9683814 | 2.7588248 |
| 95 | 13.459443 | 2.9111261 | 2.835165 |
| 96 | 13.549813 | 2.8526893 | 2.913081 |
| 97 | 13.639578 | 2.7930548 | 2.9925935 |
| 98 | 13.817319 | 2.6701274 | 3.1564968 |
| 99 | 13.905313 | 2.6068015 | 3.2409313 |
| 100 | 13.99273 | 2.542212 | 3.3270504 |
| 101 | 14.079581 | 2.4763424 | 3.414877 |
| 102 | 14.165872 | 2.4091756 | 3.5044327 |
| 103 | 14.251609 | 2.340695 | 3.5957403 |
| 104 | 14.421454 | 2.1997225 | 3.7837033 |
| 105 | 14.505574 | 2.1271968 | 3.8804045 |
| 106 | 14.58917 | 2.053288 | 3.9789493 |
| 107 | 14.672245 | 1.9779788 | 4.0793614 |
| 108 | 14.754807 | 1.9012518 | 4.1816645 |
| 109 | 14.918421 | 1.7434722 | 4.392037 |
| 110 | 14.999482 | 1.6623846 | 4.500154 |
| 111 | 15.080055 | 1.579807 | 4.610257 |
| 112 | 15.160147 | 1.495722 | 4.7223706 |
| 113 | 15.318904 | 1.322956 | 4.9527254 |
| 114 | 15.39758 | 1.2342386 | 5.0710154 |
| 115 | 15.475797 | 1.1439401 | 5.191413 |
| 116 | 15.630869 | 0.9585259 | 5.438632 |
| 117 | 15.707734 | 0.8633738 | 5.5655017 |
| 118 | 15.784159 | 0.7665674 | 5.6945767 |
| 119 | 15.860146 | 0.66808856 | 5.825882 |
| 120 | 16.01081 | 0.46606156 | 6.095251 |
| 121 | 16.08548 | 0.3625037 | 6.2333283 |
| 122 | 16.233175 | 0.15070412 | 6.515728 |
| 123 | 16.284365 | 0.07508062 | 6.616559 |
| 124 | 16.370007 | -1.4941694e-24 | 6.7166667 |
| 125 | 16.514563 | -1.8464385e-26 | 6.7166667 |
| 126 | 16.604631 | -6.1577643e-27 | 6.7166667 |
| 127 | 16.739735 | -2.053659e-27 | 6.7166667 |
| 128 | 16.942389 | -6.8492795e-28 | 6.7166667 |
| 129 | 17.24637 | -2.2843835e-28 | 6.7166667 |
| 130 | 17.702343 | -7.619005e-29 | 6.7166667 |
| 131 | 18.369009 | -2.5411517e-29 | 6.7166667 |
| 132 | 19.035677 | -8.475454e-30 | 6.7166667 |
| 133 | 19.702343 | -2.8268017e-30 | 6.7166667 |
| 134 | 20 | -9.427991e-31 | 6.7166667 |
Raw data presented with 134 records.
Constant Values
| Constant | k | y | Km |
|---|---|---|---|
| Value | 0.3 | 0.75 | 0.000001 |
Settings and Hints
| Name/Source | Value | Type | |
|---|---|---|---|
| 1 | Total number of equations | 5 | Setting |
| 2 | Number of differential equations | 2 | Setting |
| 3 | Number of explicit equations | 3 | Setting |
| 4 | Reporting digits | 10 | Setting |
| 5 | Minimal License | Free - 2 | Setting |
| 6 | Elapsed time | 0.733 ms | Setting |
| 7 | Solution method | stiff | Setting |
| 8 | Independent variable accuracy. eps | 0.00001 | Setting |
| 9 | First stepsize guess. h1 | 0.02 | Setting |
| 10 | Minimum allowed stepsize. hmin | 2e-7 | Setting |
| 11 | Good steps | 167 | Setting |
| 12 | Bad steps | 16 | Setting |
| 13 | Calculated Intermediate data points | 50 | Setting |
| 14 | Version | 7.0.73 | Setting |
| 15 | #@chart_size = 428,300 | Default (array2) | |
| 16 | #@chart_interpolate = 2 | Default (integer) | |
| 17 | #@chart_curve_width = 2 | Default (integer) | |
| 18 | #@report_fix_digits = 8 | Default (integer) | |
| 19 | #@report_show_charts = true | Default (boolean) | |
| 20 | #@report_show_data_points = true | Default (boolean) | |
| 21 | #@report_show_intermediate_data_points = true | Default (boolean) | |
| 22 | #@report_show_source = true | Default (boolean) | |
| 23 | #@report_show_header = false | Default (boolean) | |
| 24 | #@report_show_settings = true | Default (boolean) | |
| 25 | #@chart_all_curves = false | Default (boolean) | |
| 26 | #@chart_curves_stiff_grouping_percent = 50 | Default (integer) | |
| 27 | #@chart_y_curves = | Default (array2) | |
| 28 | #@chart_log_scales = 000 | Default (string) | |
| 29 | #@DEQ_SOLUTION_METHOD_INDEX = 3 | Hint | |
Messages
| Severity | Description | |
|---|---|---|
| 1 | Info | -Infor- Differential variables (2) ; S, B |
| 2 | Info | -Infor- Explicit variables (3) ; k, y, Km |
| 3 | Info | -Infor- Independent variable = t |
Source
# Example 24 - Stiff ODE System
# Biological Reactors
# Verified Final Values: B=6.71667, S=0
# Ref.:Prob. 6.1 in Problem Solving in Chemical...
# Solution algorithm is explicitly set to stiff
#@ DEQ_SOLUTION_METHOD_INDEX = 3
d(S)/d(t) = -k * y * B * S / (Km + S)
d(B)/d(t) = k * B * S / (Km + S)
k = 0.3
y = .75
Km = 1.e-6
t(0) = 0
S(0) = 5
B(0) = 0.05
t(f) =20
# Biological Reactors
# Verified Final Values: B=6.71667, S=0
# Ref.:Prob. 6.1 in Problem Solving in Chemical...
# Solution algorithm is explicitly set to stiff
#@ DEQ_SOLUTION_METHOD_INDEX = 3
d(S)/d(t) = -k * y * B * S / (Km + S)
d(B)/d(t) = k * B * S / (Km + S)
k = 0.3
y = .75
Km = 1.e-6
t(0) = 0
S(0) = 5
B(0) = 0.05
t(f) =20