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MathGroup Archive 2007

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Re: How to use the Simpson 1/3 rule to write this program

  • To: mathgroup at smc.vnet.net
  • Subject: [mg76195] Re: How to use the Simpson 1/3 rule to write this program
  • From: dh <dh at metrohm.ch>
  • Date: Thu, 17 May 2007 06:11:36 -0400 (EDT)
  • References: <f2ek5i$nq$1@smc.vnet.net>


Hi Evanescence,

Note that only K depends on z, therefore, only this function needs 

integration.

First we create the x arguments for the terms that will be multiplied by 

2 and 4. Then we apply the function K to these values, make a list of 

all terms, flatten the list for summation and sum it:

x4=Table[-0.5+i,{i,1,32}];

x2=Table[i,{i,1,31}];

int=(1/6){K[x,0],(2 K[x,#]&/@x2),(4 K[x,#]&/@x4),K[x,32]} // Flatten // 

Total

hope this helps, Daniel



Evanescence wrote:

> Hello Dear all:

> My questions are as follows:

> First I have some functions are as follows:

> K[z_,x_] is a function of z and x.

> B[x_,y_] is a function of x and y.

> F[x_] is a function of x.

> Z[x_] is a function of x.

> A[x_,y_] is a function of x and y.

> G[x_] is a function of x.

> U[x_] is a function of x.

> 

> Then I have a integration as follows:

> L[x_,y_,z_]:=(x*K[z,x])*(B[x,y]*F[x]*Z[x]+2*(A[x,y]-B[x,y]*G[x])*U[x])

> L[x,y,z] integrate to x , and the upper limit is 32 , the lower limit

> is 0

> So the integration form actually is a function of y and z.

> 

> Now I want to use Simpson 1/3 rule to repreaent the integration , so

> the integration becomes as follows

> (Assume I use the division is 1/2)

> W[y_,z_]:=(1/3)*(32-0/64)*(0+4(((1/2)*K[z,

> 1/2])*(B[1/2,y]*F[1/2]*Z[1/2]+2*(A[1/2,y]-B[1/2,y]*G[1/2])*U[1/2]))+

>                           2(((1)*K[z,1])*(B[1,y]*F[1]*Z[1]+2*(A[1,y]-

> B[1,y]*G[1])*U[1]))+

>                           4(((3/2)*K[z,

> 3/2])*(B[3/2,y]*F[3/2]*Z[3/2]+2*(A[3/2,y]-B[3/2,y]*G[3/2])*U[3/2]))+

>                           2(((2)*K[z,2])*(B[2,y]*F[2]*Z[2]+2*(A[2,y]-

> B[2,y]*G[2])*U[2]))+

>                           4(((5/2)*K[z,

> 5/2])*(B[5/2,y]*F[5/2]*Z[5/2]+2*(A[5/2,y]-B[5/2,y]*G[5/2])*U[5/2]))+

>                            .............................................................................................................

> +

>                           4(((63/2)*K[z,

> 63/2])*(B[63/2,y]*F[63/2]*Z[63/2]+2*(A[63/2,y]-

> B[63/2,y]*G[63/2])*U[63/2]))+

>                           (((32)*K[z,

> 32])*(B[32,y]*F[32]*Z[32]+2*(A[32,y]-B[32,y]*G[32])*U[32])))

> 

> My question is how to writr a computer program to represent W[y_,z_]

> and I can set the upper limit ,the lower limit,and the division in

> myself.

> 

> Thank you for your advice and answer!!

> Evanescence 2007 5 15.

> 

> 




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