PolymathPlus Report
📉   Differential Equations 2022-04-01 12:44 

# Example 10 - ODE System
# Set of consecutive reactions. Verified Final
# A,B,C Values: 0.049787, 0.047308 , 0.902905

A' = -k1*A
B' = k1*A - k2*B
C' = k2*B

k1 = 1
k2 = 2
A|1
B|0
C|0
t|0:3


Calculated values

  Variable Initial value Minimal value Maximal value Final value
1 A 1 0.04978707 1 0.04978707
2 B 0 0 0.24994676 0.04730832
3 C 0 0 0.90290462 0.90290462
4 k1 1 1 1 1
5 k2 2 2 2 2
6 t 0 0 3 3

Integration chart

 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.6 1.2 1.8 2.4 3 t A B C

Formatted equations

  d A ( ) d t ( ) = k 1 A
  d B ( ) d t ( ) = k 1 A k 2 B
  d C ( ) d t ( ) = k 2 B
  k 1 = 1
  k 2 = 2

Differential equations

1 d(A)/d(t) = -k1*A
2 d(B)/d(t) = k1*A - k2*B
3 d(C)/d(t) = k2*B

Explicit equations

1 k1 = 1
2 k2 = 2

General

Total number of equations 5
Number of differential equations 3
Number of explicit equations 2
Reporting digits 10
Elapsed time 0.00 sec
Solution method RKF_45
Step size guess. h 1E-06
Truncation error tolerance. eps 1E-06
Calculated Intermediate data points 50

Calculated data points

    t A B C k1 k2
1 0 1 0 0 1 2
2 0.12726121 0.88050364 0.10521698 0.01427938 1 2
3 0.18901368 0.82777518 0.14256343 0.02966139 1 2
4 0.26157595 0.7698374 0.17718778 0.05297482 1 2
5 0.30188983 0.73941952 0.19267829 0.06790219 1 2
6 0.39065893 0.67661089 0.21880859 0.10458051 1 2
7 0.43865893 0.6449007 0.22900379 0.12609551 1 2
8 0.48665893 0.61467665 0.23684927 0.14847408 1 2
9 0.58265893 0.55841162 0.24658808 0.1950003 1 2
10 0.63065893 0.53224098 0.24896052 0.2187985 1 2
11 0.67865893 0.50729686 0.24994676 0.24275638 1 2
12 0.72665893 0.48352178 0.24972847 0.26674975 1 2
13 0.82265893 0.43926214 0.24631091 0.31442695 1 2
14 0.87065893 0.41867558 0.24338634 0.33793808 1 2
15 0.91865893 0.39905384 0.23980988 0.36113628 1 2
16 0.96665893 0.3803517 0.23568429 0.38396401 1 2
17 1.0626589 0.34553583 0.22614082 0.42832334 1 2
18 1.1106589 0.32934188 0.22087581 0.44978232 1 2
19 1.1586589 0.31390687 0.21536935 0.47072378 1 2
20 1.2066589 0.29919524 0.20967745 0.4911273 1 2
21 1.3026589 0.27180811 0.19792846 0.53026342 1 2
22 1.3506589 0.2590695 0.19195249 0.54897801 1 2
23 1.3986589 0.24692789 0.18595451 0.5671176 1 2
24 1.4466589 0.23535532 0.17996319 0.58468149 1 2
25 1.5426589 0.21381184 0.16809634 0.61809183 1 2
26 1.5906589 0.20379128 0.1622604 0.63394832 1 2
27 1.6386589 0.19424036 0.15651104 0.6492486 1 2
28 1.6866589 0.18513705 0.15086132 0.66400163 1 2
29 1.7826589 0.16819035 0.13990235 0.6919073 1 2
30 1.8306589 0.1603079 0.13460928 0.70508282 1 2
31 1.8786589 0.15279488 0.1294486 0.71775652 1 2
32 1.9266589 0.14563396 0.12442471 0.72994133 1 2
33 2.0226589 0.13230321 0.11479907 0.75289771 1 2
34 2.0706589 0.12610266 0.11020078 0.76369656 1 2
35 2.1186589 0.12019271 0.10574642 0.77406087 1 2
36 2.1666589 0.11455973 0.1014358 0.78400447 1 2
37 2.2626589 0.10407339 0.09324212 0.80268448 1 2
38 2.3106589 0.09919587 0.08935605 0.81144809 1 2
39 2.3586589 0.09454693 0.08560781 0.81984526 1 2
40 2.4066589 0.09011588 0.08199501 0.82788912 1 2
41 2.5026589 0.08186703 0.07516482 0.84296815 1 2
42 2.5506589 0.07803023 0.07194152 0.85002825 1 2
43 2.5986589 0.07437325 0.06884187 0.85678488 1 2
44 2.6466589 0.07088766 0.0658626 0.86324974 1 2
45 2.7426589 0.06439889 0.06025167 0.87534944 1 2
46 2.7906589 0.06138076 0.05761316 0.88100609 1 2
47 2.8386589 0.05850407 0.05508135 0.88641458 1 2
48 2.8866589 0.05576221 0.05265278 0.89158501 1 2
49 2.9826589 0.05065796 0.04809173 0.90125031 1 2
50 3 0.04978707 0.04730832 0.90290462 1 2