## 530 Reputation

8 years, 138 days

## Good idea...

Thank you, very much.

## thank you...

I added few lines... I am surprised that using chebyshev polynomial expansion of   f(x,t) with respect x , ( t is a parameter)  and the function does not coincide at (0,t)  ( here I fixed x=0).

New_version_and_question.mw

Whereas if we use  taylor(f(x,t), x=0, 7), we see that the value of f at x=0 is always zero, BUT using chebyshev expansion is not the case
Maybe you can help me to solve this problem
thank you

## @Carl Love  The method used is Ado...

The method used is Adomain decomposition method, as semi analytical method to find an approximate solution.

Please, try to change  the value of the soucre function f in the IVPs, there is a big difference between ADM solution and exact solution

## @tomlesliethank you for message. Th...

@tomleslie

thank you for message.
This the main, idea, but there is someting missing.
I found the same idea in the following link

I hope we can try to modify the code

thank you

## idea...

Thank you.
But, I would like to convert the heat equaitons to a system of ODEs, this can be done using finite difference only in space ( for both x and y), central finite difference, in this case, we get a system of ODEs.
for example, uxx(x,y,t) approximated by (u(x[i+1],y[j],t) -2*u(x[i],y[j],t)+ u(x[i-1],y[j],t))/dx^2

the same for uyy, approximated by

(u(x[i],y[j+1],t) -2*u(x[i],y[j],t)+ u(x[i],y[j-1],t))/dy^2
for simplicity, ley hx=hy then we get a system of ODEs:
x is vector from 0 to 1 with step size dx.
y is vector from 0 to 1 with step size dy.
Nx=length(x), Ny =length(y)

diff(u(x,y,t),t)= (u(x[i+1],y[j],t) -2*u(x[i],y[j],t)+ u(x[i-1],y[j],t))/dx^2 + (u(x[i],y[j+1],t) -2*u(x[i],y[j],t)+ u(x[i],y[j-1],t))/dy^2

so, we look now to the previous equations ( system of ODEs) as system of ODEs, at each position x[i], y[j], I think we can apply RK4

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## why its a strict global minimizer...

@Zeineb

strictly positive if (x,y,z) different to  (log(2)/4 , log(2)/4, log(2)/4)
so in this case i can say, the (log(2)/4 , log(2)/4, log(2)/4)  is strict global minimizer

why its a strict global minimizer  , which argument allows us to say that this point is strit global minimizer

## strictly positive...

strictly positive if (x,y,z) different to  (log(2)/4 , log(2)/4, log(2)/4)
so in this case i can say, the (log(2)/4 , log(2)/4, log(2)/4)  is strict global minimizer

## @Carl Love Thank you for your messa...

Comparing The value of the sixth iteration between maple and https://planetcalc.com/7748/

There is a big difference between them.

Which value of the sixth iteration can be taken as result if we want an approximate root after six iteration

Thank you

## @dharr  Please try this code, ...

I get always undefined integrals

compute_integral.mw

## @dharr  unfortunately,  the c...

unfortunately,  the code give me undefined integral

Moreover I tried to comoute

int ( (x-1)*sin(log(x)),x=0..2)

always undefinite integrals

## @tomleslie  I use the codes from&n...

I use the codes from
http://www.maths.qmul.ac.uk/~wj/MTH5110/notes/MAS235_lecturenotes1.pdf

Remark:
I change the input matrix A
from

A := Matrix(3, 3, [[1, 2, 1], [1, 2, 1], [1, 1, 2]]);

to

A := Matrix(3, 3, {(1, 1) = 2, (1, 2) = 1, (1, 3) = 1, (2, 1) = 1, (2, 2) = 2, (2, 3) = 1, (3, 1) = 1, (3, 2) = 1, (3, 3) = 2})

the code seems to work.

What is the difference between the two definitions of matrices.
But I obtain
HFloat(HFloat(undefined))
What does this  mean HFloat(HFloat(undefined))

## @tomleslie  thak you,  i try ...

thak you,
i try to solve the zero eigenvalue problem...
In PW can i display a table contains all iterations, that is a table with three colunms : iteration, eigenvalues and corresponding eigenvectors

## Error, (in PW) bad index into Vector...

running the code using your modification I get

Error, (in PW) bad index into Vector

## @tomleslie  Fixing in my  cod...

Fixing in my  code Nx=400 , Nt=500
I get

Warning, solution did not converge within 200 iterations

what happen!!!

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