564cf393-9f74-42a7-b1c8-74cabbc75291 53 6 9 decimal

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

t0 1 time :

http://oai.cwi.nl/oai/asset/4619/04619D.pdf

t Y f 7100171 Y 1 el * - 43 Y 2 el * + 832 Y 3 el * + (* + 10000 / 171 Y 1 el * 875 Y 2 el * - 100 / 21003 Y 3 el * - 43 Y 4 el * + (* 7 Y 5 el * + 200 / 1652 Y 2 el * 7 Y 4 el * - (* 171 Y 3 el * + 100 / 349 Y 5 el * - 86 Y 6 el Y 7 el + (* + 200 / Y 6 el 4328000 Y 8 el * + (* - 323 Y 4 el * 57 Y 5 el * + 23 Y 7 el * + (* + 100 / 28000 Y 6 el * Y 8 el * 181 Y 7 el * - 100 / 28000 Y 6 el * Y 8 el * - 181 Y 7 el * + 100 / 81 mat :

IC 1000000 0.0057 81 mat :

3 possible robust solvers. # # # # # dn_AdamsMoulton 3 min ≡ # # # # # dn_ExplicitRK45 2 min ≡ # # # # # dn_GearsBDF 20 sec ≡ 31 line

5 possible robust solvers. # # # # # mwode113 2.5 min ≡ # # # # # mwode15s 40 sec ≡ # # # # # mwode23 2.5 min ≡ # # # # # mwode23s 50sec ≡ # # # # # mwode45 3 min ≡ 51 line

Sol IC 03221000 t Y f dn_GearsBDF :

X Sol 1 col : C Sol 6 col : D Sol 7 col : 31 line

X C augment X D augment 2 1 sys

Rkadapt: adequate for these 3 pairs reactions sol IC 0101000 t Y f dn_GearsBDF :

X sol 1 col : U sol 2 col : V sol 5 col : W sol 3 col : Z sol 4 col : A sol 8 col : B sol 9 col : 71 line

1 time t0 - 39.2 sec *

X U augment X V augment 2 1 sys X W augment X Z augment 2 1 sys X A augment X B augment 2 1 sys

A difficult/uncertain case

t y f 3250341 y * - 9 t * + (* + 3250341 y * 9 t * + (* - / :

Whether the integration is right/wrong ? Good question, I have no answer. It could be the integrator survives in shorter range [<15]. This example from Yuk [Ru.] Mathsoft Collaboratoty, Mathcad 11 [2004].

t Y D t Y 1 el f :

N 328649129513 mat ≡

Sanity Mathcad 11 N=500 pts rkfixed.
Rkadapt fails miserably ! S 00301295 t Y D rkfixed :

x y f 3250341 y * - 9 x * + (* + 3250341 y * 9 x * + (* - / :

x y f 0 ≡ y solve maple 325027 x * + 123 /

x datum 26.423 :

Useless solvers. # # # # # dn_AdamsMoulton does not compute ≡ # # # # # dn_ExplicitRK45 NFG ≡ # # # # # dn_GearsBDF crashes Smath ≡ # # # # # dn_ImplicitRK5 does not compute ≡ 41 line

ONE  possible limited solver. # # # # # mwode113 does not stop compute ≡ # # # # # mwode15s upper limit 15.475 ≡ # # # # # mwode23 does not stop compute ≡ # # # # # mwode23s does not stop compute ≡ # # # # # mwode45 does not stop compute ≡ 51 line

Undocumented chemical reaction

S 1 col S 2 col augment x datum 2 1 sys f x datum 2 1 sys

Assumed partially solved

Valery rkfixed solves. 
Coded Mathcad "on error" t x f t x 1 el (3.5^^t x 2 el (1^^+ t x 1 el (2^^t x 2 el (0.25^^+ 21 mat :

t0 1012 -^: t1 2 : N 705 : 31 line

v 0.5 121 mat :

Matlab "ode" solvers sol v t0 t1 N t x f mwode23 :

Useless solvers: all suffer some sort of unsanity # # # # # dn_AdamsMoulton Excessive work ≡ # # # # # dn_ExplicitRK45 Result above max ≡ # # # # # dn_GearsBDF index outside bounds ≡ # # # # # dn_ImplicitRK5 step size becomes too small ≡ 41 line

4  possible solvers: solutions meet "closely". # # # # # mwode113 solutions meet ≡ # # # # # mwode15s solutions meet ≡ # # # # # mwode23 solutions meet ≡ # # # # # mwode23s solutions meet ≡ # # # # # mwode45 NFG 't'  not defined ≡ 51 line

X sol 1 col : discretised variable of integration ≡ sol_1 X sol 2 col augment : function ≡ sol_2 X sol 3 col augment : 1rst derivative ≡ 31 line

Undocumented chemical reaction.

sol_1 sol_2 2 1 sys

sol sol rows row 1.177 2.52 2.525 13 mat