43157786-5209-4bbc-ae90-086b85531ffa 29 4 5 decimal

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

x f 425 7.73 101^/ x * + 1.69 103^/ x 2^* - 2.22 106^/ x 3^* + :

600.6 f 760.6

x f 66613002738 x - / + (- 0 ≡ x 590610 solve 600.6

x f 666 13002 738 x - / + 2 1 sys

x ca 425 7.73 101^/ x * + 1.69 103^/ x 2^* - 2.22 106^/ x 3^* + x 600.6 ≤ 66613002738 x - / + x 600.6 735 ltle 54517820 x 731 - / + x 735900 ltle 650 cases :

t ca 425 7.73 101^/ t * + 1.69 103^/ t 2^* - 2.22 106^/ t 3^* + 0 t ≤ (t 600.6 ≤ (* / 66613002738 t - / + 600.6 t ≤ (t 735 ≤ (* / 54517820 t 731 - / + 735 t ≤ (t 900 ≤ (* / 650900 t ≤ (t 1200 ≤ (* / 41 mat :

54517820740731 - / + 2525

x ca 1 el x ca 2 el x ca 3 el x ca 4 el 4 1 sys

d.p 0.01 :

ρ.p 350 :

c.p 1200 :

λ.p 0.12 :

ratio.Ap_V 107102^* :

THESE ARE THE VALUES USED IN THE EXAMPLE I'M TRYING TO MIMIC

INNDATA

Densitet stål ρ.a 7850 :

Standard temperatur-tidkurve t θ.g 203458 t * 1 + log10 * + :

x θ.g x diff 276018 x * + (10 ln * /

t Δθ.g 276018 t * + (10 ln * / :

x θ.g 0 x ≤ ( x 1200 ≤ ( * / 100 x Δθ.g 0 x ≤ ( x 1200 ≤ ( * / * 2 1 sys x Δθ.g 0 x ≤ ( x 1024 ≤ ( * /

θ.a φ c.p ρ.p * θ.a ca 1 el ρ.a * / d.p * ratio.Ap_V * c.p ρ.p * θ.a ca 2 el ρ.a * / d.p * ratio.Ap_V * c.p ρ.p * θ.a ca 3 el ρ.a * / d.p * ratio.Ap_V * c.p ρ.p * θ.a ca 4 el ρ.a * / d.p * ratio.Ap_V * 41 mat :

t Φ t φ 1 el 10 / 1 - exp t φ 2 el 10 / 1 - exp t φ 3 el 10 / 1 - exp t φ 4 el 10 / 1 - exp 41 sys :

x φ 1 el x φ 2 el x φ 3 el x φ 4 el 4 1 sys x Φ 1 el x Φ 2 el x Φ 3 el x Φ 4 el 4 1 sys

θ.a φ

Φ θ.a φ 1 el 10 / 1 - exp θ.a φ 2 el 10 / 1 - exp θ.a φ 3 el 10 / 1 - exp θ.a φ 4 el 10 / 1 - exp 41 sys :

ca 425 7.73 101^/ θ.a * + 1.69 103^/ θ.a 2^* - 2.22 106^/ θ.a 3^* + 66613002738 θ.a - / + 54517820 θ.a 731 - / + 65041 mat :

join 059673074090051 mat :

init 201265252565041 mat :

pts 14050706041 mat :

steps 5 :

t.final 360 :

collect the piecewise DE ... export vector algo style  d(t,θ.a) i 1 ca length range d i el λ.p ratio.Ap_V * d.p ca * ρ.a * 1 t Φ 3 / + (* / t θ.g θ.a - (* t Φ t Δθ.g * - : for

solving vector t θ.a d d :

t0 1 time :

collect the piecewise DE solutions from incremented "for loop" s 1 : (auto-incrementing counter, accumulates sols in Res[s] ≡ i 2 join length range Res s el init s el join s el join i el pts s el t θ.a d s el dn_GearsBDF : s s 1 + : 21 line for 21 line

1 time t0 - 0 s *

plot Res 1 el Res 2 el Res 3 el Res 4 el x θ.g x join 1 el join 5 el lele / 51 sys :

plot

t θ D λ.p ratio.Ap_V * d.p t ca 1 el * ρ.a * 1 t Φ 1 el 3 / + (* / t θ.g θ - (* t Φ 1 el t Δθ.g * - λ.p ratio.Ap_V * d.p t ca 2 el * ρ.a * 1 t Φ 2 el 3 / + (* / t θ.g θ - (* t Φ 2 el t Δθ.g * - λ.p ratio.Ap_V * d.p t ca 3 el * ρ.a * 1 t Φ 3 el 3 / + (* / t θ.g θ - (* t Φ 3 el t Δθ.g * - λ.p ratio.Ap_V * d.p t ca 4 el * ρ.a * 1 t Φ 4 el 3 / + (* / t θ.g θ - (* t Φ 4 el t Δθ.g * - 41 mat :

t.12 t.init - N / 0.596

init1 20 :

t.init 0 :

t.12 596 :

N 1000 :

sol_1 init1 t.init t.12 N t θ D 1 el dn_GearsBDF :

solrkfix 00600150 t dummy D 1 el Rkadapt :

solrkfix 2 1 sys

3 appVersion 0.98.6179 ≡

Rkadapt much less points
up to the junction [600] dn_GearsBDF Rkadapt ≡

solrkfix 151 row 600126212 mat

init2 1262 :

t.12 600 :

t.23 730 :

N 1000 :

sol_2 init2 t.12 t.23 N t Y D 2 el Rkadapt :

t.23 t.12 - N / 0.13

Smath ODE librairies

Intel solvers

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

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

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

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