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

d3529ed5-0e6a-4390-8441-9a28c0d0bbe8 6 4 5 decimal

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

t f t 1.5^exp 1 - (7.170 / 6.309 * 105 -^* :

a 0 :

b 7.17 :

a b n trap b a - n / 2 / a f b f + (* b a - n / a k b a - n / * + f k 1 n 1 - sum * + (:

maxerr 103 -^:

n 2 :

∫ a b n trap :

ε ∫ :

∫

ε abs maxerr > n 2 n * : h b a - n / : dint a b n trap : ε dint ∫ - 15 / : ∫ dint : iter n : 61 line while

x f 7.17 2000 7.17 200 - 2 2 mat 2 1 sys

acc 10000 = MCD 11 t f t a b int 486.0482737

iter 4096

ε 0.0003931 -

Result dint ε + 486.049846

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

Basic Romberg-Simpson ... integration acc from options f a b 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^- (* : 32 / b a - (* w G w 01 int * 31 line eval :

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 
Integration accuracy from user command line 'n' f a b n ∫kernel 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 :

rejected integrator ... accepted erf(x) x f 0 x erf + :

x f

x f x erf :

x f vectorize x 010000000 int 9.9998 106^*

f 01000000010 ∫kernel 1107^*

Test function x f x sqrt exp :

∫kernel

sanity check the quadruplet Mathcad 11 Adaptive 5.40752818465632 ≡ Technical accuracy 5.40752818465627 ≡ Smath ∫kernel 5.40752818465635 ≡ Smath Integrator 5.407581 ≡ 41 line

a 0 :

b 2 :

f a b 2000 ∫kernel 5.40752818465635

a b n trap b a - n / 2 / a f b f + (* b a - n / a k b a - n / * + f k 1 n 1 - sum * + (:

maxerr 108 -^:

n 2 :

∫ a b n trap :

ε ∫ :

∫

ε abs maxerr > n 2 n * : h b a - n / : dint a b n trap : ε dint ∫ - 15 / : ∫ dint : iter n : 61 line while

x f 1 1 sys

t f t a b int 5.407528103

iter 65536

ε 4.2572536 109 -^*

Result dint ε + 5.407528154

jmG: 20230516