## 50 Reputation

19 years, 167 days
Attock, Pakistan

## Have a look now.....

Thanks for the suggestion, I have completed as per adviced.
My aviailable physical memory is 4GB

non_linear_P2_last_q.mw

## Sorry for the delay...

I was trying some ways around and had some success but here is the sheet non_linear_P1.mw .

Please let me know in case of any ambiguity.

God bless you!!!

## another one.....

Is there any way to change the limits of integrals in the eq7?

I am interested in converting the limits to x[i]..x[i+1].

Though at this point, I am doing the following but I think there has to be some better way.

`eq8:=eval(eq7, [a[j]= 0,  a[j+1/2]= 0,  a[j+1]= 0]):eq9:=eq7-eq8=eq8;`
`eq10:=subs(phi[i](r)=phi[j](r), eq9):collect(eq10,int);`
`eq11:=subs({int(diff(phi[j](r),r)*phi[j](r),r=1..delta)=`
`int( diff(phi[j](r),r)*phi[j](r),r=x[i]..x[i+1]),int(diff(phi[j](r),r)*phi[j+1](r),r=1..delta)`
`=int( diff(phi[j](r),r)*phi[j+1](r),r=x[i]..x[i+1]), int(diff(phi[j](r),r)*phi[j+1/2](r),`
`r=1..delta)=int( diff(phi[j](r),r)*phi[j+1/2](r),r=x[i]..x[i+1]),`
` int(diff(phi[j+1/2](r),r)*phi[j](r),r=1..delta)=int( diff(phi[j+1/2](r),r)*phi[j](r),`
`r=x[i]..x[i+1]) }, eq10):`
` `
`sorry therse x[i]'s has to be r[i]'s`

## Thanks for the comment...

I think 'i' has to be unassigned, though I can see that implicitly definig 'i' would not be a problem, since,

my mesh in the latter case is ..., x[i]<x[i+1/2]<x[i+1], ...

,the integrals are for the ith element stiffness matrix, in the case of 1D problem with quadratic basis functions.

## Another small question regarding the sam...

I have the following code which is working fine but I am not satisfied with the implementation, any suggestion to make it more aesthetic.

`restart:interface(rtablesize=infinity):N:=3:K:=Matrix(N):x[i+1/2]:=x[i]+h/2:x[i+1]:=x[i]+h:phi[i]:=piecewise(t>=x[i] and t<=x[i+1],1-3*((t-x[i])/h)+2*(((t-x[i])^2)/h)):phi[i+1/2]:=piecewise(t>=x[i] and t<=x[i+1], 1-4* (((t-x[i+1/2])^2)/h),0):phi[i+1]:=piecewise(t>=x[i] and t<=x[i+1],1+3*(t-x[i+1])/h+2*((t-x[i+1])^2)/h,0):K[1,1]:=int(diff(phi[i],t)*diff(phi[i],t), t=x[i]..x[i+1])assuming h>0:K[2,2]:=simplify(int(diff(phi[i+1/2],t)*diff(phi[i+1/2],t), t=x[i]..x[i+1])) assuming h>0:K[3,3]:=int(diff(phi[i+1],t)*diff(phi[i+1],t), t=x[i]..x[i+1]) assuming h>0:K[1,2]:=simplify(int(diff(phi[i],t)*diff(phi[i+1/2],t), t=x[i]..x[i+1])) assuming h>0:K[1,3]:=simplify(int(diff(phi[i],t)*diff(phi[i+1],t), t=x[i]..x[i+1])) assuming h>0:K[2,1]:=simplify(int(diff(phi[i+1/2],t)*diff(phi[i],t), t=x[i]..x[i+1])) assuming h>0:K[2,3]:=simplify(int(diff(phi[i+1/2],t)*diff(phi[i+1],t), t=x[i]..x[i+1])) assuming h>0:K[3,1]:=simplify(int(diff(phi[i+1],t)*diff(phi[i],t), t=x[i]..x[i+1])) assuming h>0:K[3,2]:=simplify(int(diff(phi[i+1],t)*diff(phi[i+1/2],t), t=x[i]..x[i+1])) assuming h>0:K;`

## The execution is taking too much time....

`restart;N:=10:K:=Matrix(N-1):for i from 1 to N do phi[i]:=piecewise(t>=x[i-1] and x[i]>t, (t-x[i])/(h), x[i]<t and t<=x[i+1], (x[i+1]-t)/(h), 0):end do:for i from 2 to N-2 do    V1:=Int(diff(phi[i], t)*diff(phi[i], t), t=x[i]..x[i+1]):    V2:=Int(diff(phi[i], t)*diff(phi[i+1], t), t=x[0]..x[N]):    L1:=value(V1) assuming x[i-1]<x[i],x[i]<x[i+1];    M1:=algsubs(x[i]-x[i-1]=h, L1);    K[i,i]:=algsubs(x[i+1]-x[i]=h, M1);    L2:=value(V2) assuming seq(x[i-1]<x[i], i=1..N);    M2:=algsubs(x[i]-x[i-1]=h, L2);    K[i,i+1]:=algsubs(x[i+1]-x[i]=h, M2);    K[i-1,i]:=K[i,i+1]; end do:K;`
` `
`So I have got this, its runing pretty as expected except the last statement`
` > K[i-1,i]:=K[i,i+1].`
`There is just one problem that the algorithim is runing too slow even for this small value of N,`
` since I am mainly interested in runing this for some large value of N, `
`therefore I would really appreciate I someone could suggest some thing to make it fast.`

## The representation of phi[i] phi[i]:=t-...

The representation of phi[i]

phi[i]:=t->piecewise(t>=x[i-1] and x[i]>t, (t-x[i])/(h), x[i]<t and t<=x[i+1], (x[i+1]-t)/(h), 0);

produces the same output but in that case maple does not use heavside function but its definition.

## ......

phi[i]:=piecewise(t>=x[i-1] and x[i]>t, (t-x[i])/(h), x[i]<t and t<=x[i+1], (x[i+1]-t)/(h), 0);

## @Carl Love Thanks for looking into...

Thanks for looking into it.

here is the command

phi[i]:=piecewise(t>=x[i-1] and x[i]>t, (t-x[i])/(h), x[i]

## Have you already looked into the help, e...

I tried it very extensively but you may agree that Maple online help browser isn't that good, I don't know whether they have done some thing in newer versions or not.

Afterwards after using bing.com, I came across some maple sheet by Dr. Robert Lopez(http://www.maplesoft.com/applications/view.aspx?SID=1742), the author is trying to compare ways to do by parts integration in maple, a nice overview of by parts integration in maple.

## I have figure that out. with(Integratio...

I have figure that out.

with(IntegrationTools):

integral_1:=  int( diff( u(x), x\$2) * v(x), x=0..1):

Integral_2:= Parts(integral_1, v(x)) = D(u)(1)*v(1) - D(u)(0)*v(0) - int( diff(u(x), x) * diff(v(x), x), x=0..1)

subs({v(1) = 0, v(0)= 0}, Integral_2 ) = - int( diff(u(x), x) * diff(v(x), x), x=0..1)

This completes what I was tyring to accomplished.

I do have little point, I know define() is more powerful as compared to subs()  but I was unable to use that. Would some body help?

## Thanks guys for kind words. The two exp...

Thanks guys for kind words.

The two experts with complete different nature of expertise.

## Thanks!!...

Thankyou very much!

Is it possible in maple to make the coordinate axes thick (or to rephrase my question, do we have a control on the thickness or colour of the coordinate axis )? as we do have a control on the thickness of the curve in maple.

 Page 1 of 1
﻿