2733db63-e93b-4ac1-9e29-d01618afbd8b 9 4 5 decimal

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Simulating a test example for stiff methods. The system consists of an autocatalytic chemical process with three chemical species (A, B and C) participating in three reactions of the form: k_1 k_2 k_3 A → B B + C → A + C 2B → C + B The rate constants are:

k.1 0.04 s 1 -^* :

k.2 104^L mol s * / * :

k.3 3107^* L mol s * / * :

Here we denote the concentrations of the three chemical species (A, B and C) with a vector z: z_1 = [A], z_2 = [B], and z_3 = [C]

The initial concentration:

A.ini 1 mol * L 1 -^* :

(all other are zero)

z.initial A.ini L mol / * 0031 mat :

z z.initial :

z 10031 mat

To avoid negative concentrations during integration we define the function "c":

conc c conc 0 > conc mol L / * 0 mol L / * if :

The system of ordinary differential equations is:

t z D k.1 z 1 el c * - k.2 z 2 el c * z 3 el c * + (s L * mol / * k.1 z 1 el c * k.2 z 2 el c * z 3 el c * - k.3 z 2 el c (2^* - (s L * mol / * k.3 z 2 el c (2^* (s L * mol / * 31 mat :

Note that units are removed.

Now try to solve this thing.

t.final 100 :

n.steps 10 :

res z.initial 0 t.final n.steps t z D Rkadapt :

The results are wrong. The second column should not have negative values!

res 010010 0.6 0.4 020 0.2 0.8 030 0.2 - 1.2 040 0.6 - 1.6 0501 - 2060 1.4 - 2.4 070 1.8 - 2.8 080 2.2 - 3.2 090 2.6 - 3.6 01003 - 40114 mat

01 - 2031 mat D 0 1.2 108^* - 1.2 108^* 31 mat