Architecture
°ÇÃà Architecture


Numerical integration; Simpson¡Çs rule, using a cubic equation

ÀÛ¼ºÀÚ Uploader : mangsteen ÀÛ¼ºÀÏ Upload Date: 2019-06-24º¯°æÀÏ Update Date: 2019-07-16Á¶È¸¼ö View : 230

When the function f(x) is integrated with respect to the sections a and b, an approximate value can be obtained by substituting with a cubic equation. 

¡òf(x)¡Ö¡òP(x) = ((b-a)/8)*(f(a)+3*f((2a+b)/3)+3*f((a+2b)/3)+f(b))

With the interval between a and b triplicated, and letting the four points from a to b as x0, x1, x2, and x3, respectively, we get :

x0 = a, x1 = (2a+b)/3, x2 = (a+2b)/3, x3 = b

Letting fx0 = f(a), fx1 = f((2a+b)/3), fx2 = f((a+2b)/3), and fx3 = f(b), we get :

Res = ((b-a)/8)*(fx0+3*fx1+3*fx2+fx3)

If the triplicated interval is h, then h = (b-a)/3 and it is called the 3/8 formula. 
Res = (3*h/8)*(fx0+3*fx1+3*fx2+fx3)


*** Âü°í¹®Çå[References] ***

https://en.wikipedia.org/wiki/Simpson%27s_rule
Res = ((b-a)/8)*(fx0+3*fx1+3*fx2+fx3)
ÀÛ¼ºÀÚÀÇ ¼ö½Ä±×¸²ÀÌ ¾ø½À´Ï´Ù. No picture for this formula
º¯¼ö¸í Variable º¯¼ö°ª Value º¯ ¼ö ¼³ ¸í Description of the variable


¡Ø ÀÌ »çÀÌÆ®´Â ±¤°í¼öÀÍÀ¸·Î ¿î¿µµË´Ï´Ù.

¡Ú ·Î±×ÀÎ ÈÄ ¼ö½ÄÀÛ¼º ¹× Áñ°Üã±â¿¡ Ãß°¡ÇÒ ¼ö ÀÖ½À´Ï´Ù.
¡Ú To make new formula or to add this formula in your bookmark, log on please.


ÄÚ¸àÆ®

´ñ±Û ÀÔ·Â