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Write a computer program to using Simpson's rule

• To: mathgroup at smc.vnet.net
• Subject: [mg74016] Write a computer program to using Simpson's rule
• From: "Evanescence" <origine26 at yahoo.com.tw>
• Date: Tue, 6 Mar 2007 05:28:15 -0500 (EST)

Hello Dear all:
My questions are as follows:
First I definite as follows functions.
B[=A3f_, =A3b_] function of =A3f, =A3b
A[=A3f_, =A3b_] function of =A3f, =A3b
F[=A3f_] function of =A3f
G[=A3f_] function of =A3f
K[=A3i_, =A3f_] function of =A3i, =A3f
Z[=A3f_] function of =A3f
U[=A3f_] function of =A3f

Then I want to write a computer program about Simpson's 1/3 rule that
can express below function
L[=A3b_, =A3i_] :=(1/3)*((16-0)/32)*(0+4(((1/2)*K[=A3i, 1/2] )*(B[1/2,
=A3b]*F[1/2]*(Z[1/2])+2*( A[1/2, =A3b]-B[1/2, =A3b]*G[1/2])*U[1/2]))+2
(((1)*K[=A3i, 1] )*(B[1, =A3b]*F[1]*(Z[1])+2*( A[1, =A3b]-B[1 =A3b]*G[1])*U=
[1]))
+4(((3/2)*K[=A3i, 3/2] )*(B[3/2, =A3b]*F[3/2]*(Z[3/2])+2*( A[3/2, =A3b]-B[3=
/2,
=A3b]*G[3/2])*U[3/2]))
+2(((2)*K[=A3i, 2] )*(B[2, =A3b]*F[2]*(Z[2])+2*( A[2, =A3b]-B[2,
=A3b]*G[2])*U[2]))
+=2E.......................................................................
+(((16)*K[=A3i, 16] )*(B[16, =A3b]*F[16]*(Z[16])+2*( A[16, =A3b]-B[16,
=A3b]*G[16])*U[16])))

the 16 is upper limit of integration
and the 0 is lower limit of integration
subdivision is 1/2

I want to write a computer program using the Simpson's rule that can
choose the subdivision by myself(maybe can choose 0.001 or 0.002
etc...)and upper and lower limit can choose by myself too,final can
express the above function.

Thank you
Evanescence 2007 03 06

• Follow-Ups:
  • Re: Write a computer program to using Simpson's rule
    • From: Daniel Lichtblau <danl@wolfram.com>