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

1a5c7ade-d749-4b28-8d0f-0a46ef53f4f9 17 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 :

x y f3 x y < t x : x y : y t : 31 line x x - : y y - : 21 line if 11 line :

autocalc

α 0.75 :

ε 1012 -^:

k 0.25 - (k * : 1.75

x f x k + f3 :

Experiment freak plot f3(x,k) ......... SS 6179 .........

α x k + ( f3 ( * k 2 k 2 - 2 2 mat α x * k ε - ( α k ε - f * + 40 black 1 5 mat 4 1 sys

k ε - f k ε + f 12 mat 1.75 1.75 - 12 mat

Σ0 k 0 ≤ α 0 f * k abs * N/A if : Σ1 0 k ≤ 0.5 α * k ε - f * k * N/A if : 21 sys

k + (k eval ≡

α k ε - f * 1.3125

Σ0 Σ1 21 mat N/A 1.1484 21 mat