       Re: Write a computer program to using Simpson's rule

• To: mathgroup at smc.vnet.net
• Subject: [mg74045] Re: [mg74016] Write a computer program to using Simpson's rule
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Wed, 7 Mar 2007 03:14:41 -0500 (EST)
• References: <200703061028.FAA01952@smc.vnet.net>

```Evanescence wrote:
> 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*(Z)+2*( A[1, =A3b]-B[1 =A3b]*G)*U=
> ))
> +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*(Z)+2*( A[2, =A3b]-B[2,
> =A3b]*G)*U))
> +=2E.......................................................................
> +(((16)*K[=A3i, 16] )*(B[16, =A3b]*F*(Z)+2*( A[16, =A3b]-B[16,
> =A3b]*G)*U)))
>
> 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

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Daniel Lichtblau
Wolfram Research

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