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. > >