8ca8ebae-7015-4fe8-ac76-a8e49d0fece7 22 6 9 decimal

&[DATE] &[TIME] - &[FILENAME]

k1 0.5 : k2 0.25 : k3 0.1 : ω 1 : 41 line

γ1 γ2 + k1 k2 + k3 + ≡ γ1 γ2 * k1 k2 * k1 k3 * + ≡ 21 mat

Fig. 2.11 Kinetics of the two-step first-order consecutive reaction with the reversible second step [Mathcad Laplace]. http://www.biokin.com/tools/pdf/Koro11-Kinetics-Maple-Chap2.pdf

k1 10.052 : k2 14.836 : k3 4.982 : 31 line

γ1 19.818 : γ2 10.052 : ω 1 : 31 line

t A ω k1 t * - exp * :

t B k3 γ1 γ1 γ2 - (* / 1 γ1 γ2 - (/ - (γ1 t * - exp * k3 - γ2 γ1 γ2 - (* / 1 γ1 γ2 - (/ + (γ2 t * - exp * + k3 γ1 γ2 * / + (ω * k1 * :

t C k1 ω * k2 * 1 γ1 γ2 * / 1 γ2 γ1 γ2 - (* / γ2 t * - exp * - 1 γ1 γ1 γ2 - (* / γ1 t * - exp * + (* :

x A 0 x ≤ x A NOT DE if :

x B 0 x ≤ x B NOT DE if :

x C 0 x ≤ x C NOT DE if :

tmax k3 γ2 - k3 γ1 - / ln γ1 γ2 - / - :

Fig. 2.11 Kinetics of the two-step first-order consecutive reaction with the reversible second step

x A x B x C 0.11 0.336 + 15 black 1 5 mat 4 1 sys

tmax tmax B 21 mat 0.109944 0.336107 21 mat

x A x B x C 0.11 0.336 + 15 black 15 mat 41 sys

k1 k2 A---->B<====>C k3

This 'rk linear system'

t X t diff k1 t X * - ≡ t Y t diff k1 t X * k2 t Y * - k3 t Z * + ≡ t Z t diff k2 t Y * k3 t Z * - ≡ 31 line

the rk vector t X D k1 X 1 el * - k1 X 1 el * k2 X 2 el * - k3 X 3 el * + k2 X 2 el * k3 X 3 el * - 31 mat :

k1 10.052

initials init 10031 mat :

k2 14.836

k3 4.982

t 1 el 0 : start point ≡ T 1 : segment length ≡ ε 104 -^: accuracy ≡ h 0.0001 : step size ≡ 41 line

x init : A Cauchy problem ≡

tx x x cols col : 10031 mat

j t 1 el h + : j T t 1 el + h + ≤ j j h + : tx x x cols col : k1 h 3 / j tx D eval * : k2 h 3 / j h 3 / + tx k1 + D eval * : k3 h 3 / j h 3 / + tx k1 k2 + 2 / + D eval * : k4 h 3 / j h 2 / + tx 3 k1 * 9 k3 * + 8 / + D eval * : k5 h 3 / j h + tx 3 k1 * 9 k3 * - 2 / + 6 k4 * + D eval * : δ k1 92 / k3 * - 4 k4 * + 12 / k5 * - : δ min abs 5 ε * ≤ (δ max abs 5 ε * ≤ (& x x tx 12 / k1 4 k4 * + k5 + (* + augment : steps 1 x cols el j : h h 2 * : 31 line j j h - : h h 2 / : 21 line if 81 line for

result steps x stack :

result cols 22

Число значений

Angka hasil

Number of values

Prepare/extract solutions

Y x # row transpose ≡ the Y collection ≡

X steps transpose : RK_1 X x 1 row transpose augment : RK_2 X x 2 row transpose augment : RK_3 X x 3 row transpose augment : 41 line

x sol_1 0 x ≤ (x T ≤ (& RK_1 1 col RK_1 2 col x cinterp out range if :

x sol_2 0 x ≤ (x T ≤ (& RK_2 1 col RK_2 2 col x cinterp out range if :

RK_1 RK_2 RK_3 3 1 sys

x sol_3 0 x ≤ (x T ≤ (& RK_3 1 col RK_3 2 col x cinterp out range if :

Fine meshing over the canvas plot.

x sol_1 x sol_2 x sol_3 3 1 sys

Smath ODE librairies

# # # # # al_rkckadapt

Stiff/NON stiff solvers. # # # # # dn_AdamsMoulton # # # # # dn_ExplicitRK45 # # # # # dn_GearsBDF # # # # # dn_ImplicitRK5 41 line

ONE  possible limited solver. # # # # # mwode113 # # # # # mwode15s # # # # # mwode23 # # # # # mwode23s # # # # # mwode45 51 line

# # # # # Rkadapt # # # # # rkfixed # # # # # rkm9mka # # # # # rkm9mkn # # # # # rkm9st 51 line

Jacobi # # # # # mk52lfa # # # # # mk52lfn 21 line

Shadow in context wrt 'X'

k1 10 : k2 15 : k3 5 : 31 line

k1 k2 A---->B<====>C k3

the rk vector t U D k1 U 1 el * - k1 U 1 el * k2 U 2 el * - k3 U 3 el * + k2 U 2 el * k3 U 3 el * - 31 mat :

initials init 10031 mat :

sol init 01200 t U D Rkadapt :

biokin sol 1 col sol 2 col augment sol 1 col sol 3 col augment sol 1 col sol 4 col augment 31 sys :

biokin