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

44b0cb81-b3ac-42d7-a053-fafc810510a2 10 15 12 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 Int 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 :

XY char size clr plot k 1 XY rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for XY r3 r4 r5 augment 21 line :

ε 1010 -^:

x q 0 x 0 ≤ x x 2.5 ≤ 0.25 x 2.5 ε + ≤ 0.25 x 6 ≤ 22.9 x 6 ≡ x 32.7 22.9 - 7.5 6 - ε + / (* 22.9 (- x 6 ε + ≥ (x 7.5 ≤ (& 0 x 7.5 ≥ cases :

x 010 0.01 range : XY x x q vectorize augment : data XY o 3 black plot : 31 sys

data x q 2 1 sys

NOT exact [1000] x q x 0 7.5 int 35.57125

x f x q :

f 0 7.5 1000 Int 35.80072

x q 4 x 10 ≤ x x 10 ≥ cases :

x 016 0.1 range : XY x x q vectorize augment : data XY o 3 black plot : 31 sys

data

NOT exact [100] x q x 1016 int 77.940000

x f x q :

f 1016100 Int 78.000000