<p> plotG & discretise Spline, FD cumulative </p>

652d7d2c-24c0-40f5-8ffd-2600365c00ca 11 6 9 decimal

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

f a b Int x f x a b int 32 / b a - (* w G w 01 int * ≡ memo ≡ 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 * 41 line :

Test function x f x sqrt exp :

x f 0 2 1 sys

sanity check the quadruplet Mathcad 11 Romberg 5.40752818465632 ≡ Technical accuracy 5.40752818465627 ≡ Smath Romberg 5.40752818465657 ≡ Smath Integrator 5.407526 ≡ 41 line

f 02 Int 5.40752818465657

x f x f Clear :

<p> plotG & discretise Spline, FD cumulative </p>

vx vy chr sz clr plotG n vx length : plot vx 1 el vy 1 el chr sz clr augment : i 2 n range plot plot vx i el vy i el chr sz clr augment stack : for plot 41 line :

Low step High x 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 :

data Σ FD 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 :

h 0.001 :

XY 1 1.3 1.5 2.5 2 5.2 2.5 0.8 42 mat :

X XY 1 col : Y XY 2 col : x f X Y x cinterp : 31 line

Spline 1 1.01 2.51 x f inc : data X Y . 14 red plotG : 21 line

Spline Σ 151 row 2.5 4.72486 12 mat

scalar derivative of the spline f x h deriv 0.5 x h - f x f - x h - (x - / x f x h - f - x x h - (- / + (* :

Spline Spline Σ data 3 1 sys 1 x ≤ x 2.5 ≤ & x f x h deriv out range if 1 1.3 . 14 red 1.5 2.5 . 14 red 2 5.2 . 14 red 2.5 0.8 . 14 red 4 5 mat 2 1 sys

f 1 2.5 Int 4.725