<p> ∫Adaptive(f,a,b,ε) Carlos </p>

a7da4f31-cac7-4eaa-b6f3-d3551ffd575f 17 4 5 decimal

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

stiff ... NON stiff soup ! # # # # # mwode113 # # # # # mwode15s # # # # # mwode23 # # # # # mwode23s # # # # # mwode45 51 line

Useless solvers. # # # # # al_rkckadapt # # # # # dn_AdamsMoulton # # # # # dn_ExplicitRK45 # # # # # dn_GearsBDF # # # # # dn_ImplicitRK5 51 line

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

1.73750207472565

stiff Jacobian # # # # # mk52lfa # # # # # mk52lfn 21 line

x f x 0.5 1 -^x - exp * eval : a 1018 -^: b e : 12 mat 21 sys

N 1000 :

Fail to ▲ solve

x Y D x f :

sol 0 a b N x Y D al_rkckadapt :

sol sol rows row 2.718282 1.737526 12 mat

sol 0 a b N x Y D dn_AdamsMoulton :

sol sol rows row 2.718282 1.737568 12 mat

sol 0 a b N x Y D dn_ExplicitRK45 :

sol sol rows row 2.718282 1.737519 12 mat

sol 0 a b N x Y D dn_GearsBDF :

sol sol rows row 2.718282 1.738344 12 mat

sol 0 a b N x Y D dn_ImplicitRK5 :

sol sol rows row 2.718282 1.737499 12 mat

x f x 0.5 1 -^x - exp * eval : a 1018 -^: b e : 12 mat 21 sys

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

x Y D x f :

sol 0 a b N x Y D Rkadapt :

freak ! sol sol rows row 2.718282 469.379272 12 mat

sol 0 a b N x Y D rkfixed :

freak ! sol sol rows row 2.718282 2.718283 106^* 12 mat

sol 0 a b N x Y D rkm9mka :

close ! sol sol rows row 2.718282 1.737671 12 mat

sol 0 a b N x Y D rkm9mkn :

close ! sol sol rows row 2.718282 1.737671 12 mat

sol 0 a b N x Y D rkm9st :

close ! sol sol rows row 2.718282 1.737671 12 mat

<p> ∫Adaptive(f,a,b,ε) Carlos </p>

f a b ε ∫Adaptive N 100 : sum 0 : i 1 : tol i el ε : aa i el a : h i el b a - (2 / : 51 line .... fa i el a f : fc i el a h i el + f : fb i el b f : s i el h i el fa i el 4 fc i el * + fb i el + (3 / * : L i el 1 : 51 line 13 mat above => initialise the while loop i 0 > fd aa i el h i el 2 / + f : fe aa i el 3 h i el * 2 / + f : 12 mat s1 h i el fa i el 4 fd * + fc i el + 6 / (* : s2 h i el fc i el 4 fe * + fb i el + 6 / (* : 12 mat v1 aa i el : v2 fa i el : v3 fc i el : v4 fb i el : v5 h i el : v6 ε : v7 s i el : v8 L i el : 18 mat i i 1 - : s1 s2 + v7 - abs v6 < sum sum s1 s2 + (+ : v8 N ≥ Solution Insufficient Number of Intervals : i i 1 + : aa i el v1 v5 + : fa i el v3 : fc i el fe : fb i el v4 : 14 mat h i el v5 2 / : tol i el v6 2 / : s i el s2 : L i el v8 1 + : 14 mat i i 1 + : aa i el v1 : fa i el v2 : fc i el fd : fb i el v3 : h i el h i 1 - el : s i el s1 : 16 mat L i el L i 1 - el : 61 line if if 51 line while sum 41 line 21 line eval :

x f x 0.5 1 -^x - exp * eval : a 1019 -^: b e : 12 mat 21 sys

Adaptive MCD11 1.73750207472566 ≡

Exact 1.73750207472565

t0 1 time :

11½ decials Damned good !!! f a e 0.00000000001 ∫Adaptive 1.737502074210

1 time t0 - 13.6 s *

Like most other solvers, ∫Adaptive(f,a,b,ε) converges first ... then diverges wrt ε. 'a' [zero] has some influence. Mathcad/Mathsoft zero was 'guessed' 10^{-18}