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

e35d7180-871e-4365-95ea-cec5bb100874 29 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 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 :

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

Numerical engine does not recognize > 15 D input

..... OK 
..... OK
from otherwise 9.999999999999999 q 10.000000000000001 q 5 q 31 mat 410431 mat

data

NOT exact [1000] x q x 1016 int 77.94

x f x q :

f 1016100 Int 78.000000000000100

Plot is OK
Integration OK x F 4 x sign * 0 x ≤ (x 10 ≤ (& x cases :

u F u 1015 int 62.45

x f x F :

f 1015100 Int 62.5

t q t 0 x int

h 0.01 :

Infinitesimal Derivative x h F D2 0.5 x h - F x F - x h - (x - / x F x h - F - x x h - (- / + (* (:

x h F D2 x F

T t 2 t 1 - 22 mat :

t 2 :

X 5 - 5 4.9 - range :

X t Heaviside.D T 2 1 sys x t Heaviside T 2 1 sys

1.999999 2 Dirac 22 Dirac 2.000001 2 Dirac 31 mat 0 ∞ 031 mat