<p> ∫(f,a,b,n).. Simpson/Romberg Kernel </p>

bbfb9e5c-c3b6-44bc-aae7-96bde44d15f0 69 4 5 decimal

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

Simpson Integrator in the Romberg Transform Domain [0,1] <= [a,b] ...  
... integrates  Smath ainterp(X,Y,x), cinterp(X,Y,x), cubic(x) from  l_p_c_spline f a b n ∫ w s b a - (34 / 2 w * 1 - (* 14 / 2 w * 1 - (3^* - 12 / + (* a + : w G w s f 12 w * 1 - (2^- (* : α 0 : β 1 : h β α - n / : 14 mat Simpson 13 / h 2 / α G β G + (* h α k h * + G k 1 n 1 - sum * + (* 23 / h * α h 2 / - k h * + G k 1 n sum * + eval : 32 / b a - (* Simpson * 41 line :

Identify each component

t θ.g 203458 t * 1 + log10 * + :

? ratio.Am.b_V 70102^* : ratio.Am_V 107102^* : k.sh 0.9 ratio.Am.b_V ratio.Am_V / * : 31 sys

? ρ.a 7850 : α.c 25 : σ 5.67 108^/ : 31 sys

? Φ 1.0 : ε.m 0.7 : ε.f 1.0 : 31 sys

k.sh 11 mat 0.5888 11 mat

C.a 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 :

system segments specifications

join 0 24.36475 35.7945 54.7 12051 mat :

init 2060073590041 mat :

pts 200100100100041 mat :

original 24.4 ... 35.8

collect the piecewise DE ... export vector algo style  d(t,θ.a) i 1 C.a length range d i el k.sh C.a i el ρ.a * / ratio.Am_V * α.c t θ.g θ.a - (* Φ ε.m * ε.f * σ * t θ.g (4^θ.a 4^- (* + (* : for

solving vector t θ.a d d :

t0 1 time :

collect the piecewise DE solutions from incremented "for loop" s 1 : 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 - 5 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 / 61 sys :

plot Res 1 el Res 2 el Res 3 el Res 4 el t θ.g 5 1 sys

strip from repeated junctions res_2 Res 2 el 2 Res 2 el rows 12 submatrix : res_3 Res 3 el 2 Res 3 el rows 12 submatrix : res_4 Res 4 el 2 Res 4 el rows 12 submatrix : global Res 1 el res_2 res_3 res_4 stack : Global global 1 col global 2 col augment : 51 line

global 020 0.12 20.31 0.24 21.05 0.37 22.08 0.49 23.32 0.61 24.74 0.73 26.31 72 mat

x f global 1 col global 2 col x linterp :

Low step High # fnct inc U Low High step range : i 1 U rows range f i el U i el fnct eval : for U f augment 31 line :

recast for regular tabulation New 0 0.25 120 x f inc :

New 020 0.25 21.11 0.5 23.47 0.75 26.57 1 30.2 1.25 34.24 1.5 38.61 1.75 43.27 2 48.17 2.25 53.29 2.5 58.59 2.75 64.05 3 69.66 3.25 75.4 3.5 81.26 3.75 87.22 4 93.28 4.25 99.43 4.5 105.65 192 mat

user 768 :

Θ x θ.g user - x 0120 solve : R x f user - x 0120 solve : 21 sys

New x θ.g x join 1 el join 5 el lele / 16 - user R user 2 2 mat Θ user Θ 100 - 2 2 mat R user R 100 - 2 2 mat 5 1 sys

Θ R 12 mat 18.3 40.8 12 mat

h 0.01 :

x λ 10 x ≤ (x 120 ≤ (& cases :

x h f D1 x 2 h * + f - 8 x h + f * + 8 x h - f * - x 2 h * - f + 12 h * / :

x h f D1 x λ *

x λ 120 x ≤ (x 32 ≤ (& cases :

x h f D1 x λ *

x f x 010 int 1233

f 01020 ∫ 1233

New rows 481

data Σ Finite differences Cumul Integration vx data 1 col : vy data 2 col : Y 1 el 0 : i 2 vx rows range Δx i el vx i el vx i 1 - el - : Y i el Y i 1 - el 12 / vy i 1 - el vy i el + (Δx i el * (* + : 21 line for vx Y augment 61 line :

data New :

desired 256 :

track data Σ desired row : 643911512 mat

Finite differences Cumulative Integral

16 - track 1 2 el track 1 1 el track 1 2 el 2 2 mat data Σ track 1 1 el track 1 2 el track 1 1 el 10000 - 2 2 mat 3 1 sys

evaluate symbolic ... Ctrl.
isolate to export sanity QA t θ.a d

QA [Quality Assurance] requirements

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t θ.a d 221679950582572500000000000546918 t * + log10 * + (* θ.a - (* 396962546918 t * + log10 * + (4^* θ.a 4^- (* + (* 55244051176926200500100425000773 θ.a * + (* 169 θ.a 2^* - (* 111 θ.a 3^* + (* / 21738 θ.a - (* 2500000000000546918 t * + log10 * + (* θ.a - (* 396962546918 t * + log10 * + (4^* θ.a 4^- (* + (* 157000000000002167111738 θ.a - (* + (* / 63731 - θ.a + (* 2500000000000546918 t * + log10 * + (* θ.a - (* 396962546918 t * + log10 * + (4^* θ.a 4^- (* + (* 392500000000003564109731 - θ.a + (* + (* / 632500000000000546918 t * + log10 * + (* θ.a - (* 396962546918 t * + log10 * + (4^* θ.a 4^- (* + (* 5102500000000000 / 41 mat :

optimized from above sol 200 24.36475 120 t θ.a d 1 el dn_GearsBDF 600 24.36475 35.7945 120 t θ.a d 2 el dn_GearsBDF 735 35.7945 54.7 120 t θ.a d 3 el dn_GearsBDF 900 54.7 1201200 t θ.a d 4 el dn_GearsBDF 41 sys :

join 0 24.36475 35.7945 54.7 12051 mat :

init 2060073590041 mat :

sol 1 el sol 2 el sol 3 el sol 4 el 4 1 sys

x spline sol 1 el 1 col sol 1 el 2 col x linterp 0 x ≤ (x 24.36475 ≤ (& sol 2 el 1 col sol 2 el 2 col x linterp 24.36475 x ≤ (x 35.7945 ≤ (& sol 3 el 1 col sol 3 el 2 col x linterp 35.7945 x ≤ (x 54.7 ≤ (& sol 4 el 1 col sol 4 el 2 col x linterp 54.7 x ≤ (x 120 ≤ (& cases :

°C 768 :

min x spline °C - x 0120 solve : 40.75

pointer 16 - 1286412864128 min °C 42 mat :

pointer x spline min °C + 40 black 1 5 mat 3 1 sys

°C min 12 mat 768 40.75 12 mat

is it that some of those system changes from Euro codes to codes ? 425 7.73 101^/ θ.a * + 1.69 103^/ θ.a 2^* - 2.22 106^/ θ.a 3^* + 20 θ.a ≤ (θ.a 600 ≤ (& 66613002738 θ.a - / + 600 θ.a ≤ (θ.a 735 ≤ (& 54517820 θ.a 731 - / + 735 θ.a ≤ (θ.a 900 ≤ (& 650 cases k.sh ρ.a ratio.Am_V α.c Φ ε.m * ε.f * σ * 51 mat 0.5888 78501070025 3.969 108 -^* 51 mat # @ = 12 mat