Al86

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4 years, 108 days

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These are questions asked by Al86

I have the following pertubation problem I want to use maple to expand for me.

 

We have epsilon := eps;

x(t,eps):= x_{-1}(t)/eps+x_0(t)+x_1(t)*eps

z(t,eps):=z_{-1}(t)/eps+z_0(t)+z_1(t)*eps

I want to expand a Taylor series of the following function upto some arbitray order of eps, i.e O(eps^3) or higher (depending on my mood :-)), around t=0, f(x(t,eps),z(t,eps),cos(t/eps),sin(t/eps)).

 

Anyone has any suggestion how to use maple 2017.3 to do this?

Thanks!

 

 

 

I have installed in my UBUNTU 16.04 system matlab 2018a already, I have recently acquired maple 2017.3 (through my university).

Now while trying to install maple in my computer I am at the matlab configuration option, I picked the directory where the matlab installation is situated at, and I get the following error: The directory /home/alon/MATLAB/R2018a/bin/matlab is not writable by the current user

I searched google for this occurrence of error, and found the following suggestion: https://askubuntu.com/questions/265381/how-to-make-a-directory-permanently-writable

the first answer suggests to write in the terminal the following line: sudo chmod 775 /home/alon/MATLAB/R2018a/bin/matlab

which I did but I still get after executing this line in the terminal the above error; what else can I do to fix this problem?

Thanks.

I want to use maple2015 to perform a Monte-Carlo simulation of a one dimensional Harmonic Oscillator.

Consider a particle having displacements, x=na where n is an integer, i.e 0 plus minus one, etc.

The potential energy of the particle is given by U(x)= 1/2 kx^2 = 1/2 ka^2 n^2.

For this simulation will choose ka^2 = 0.01 k_B T where k_B is Boltzmann's constant, and T is the temprature in Kelvin.

So we should perform a Monte-Carlo simulation starting from x(0)=20a, and perfroming individual steps by selecting an attmept to move x=+-a ,with equal probability, and choose whether to make the actual step according to energy change expected in that step.

I need to draw particle's position and x(t), and particle's energy E(t).

After that I need to calculate and draw the autocorrelation functions \phi_x(t) and \phi_E(t).

I found some code that might help me, but I am nor sure how to implement the above two lines on maple; your help is appreciated.

http://pubs.acs.org/doi/suppl/10.1021/ed100414p/suppl_file/ed100414p_si_001.pdf

 

I have the PDE u_{xx}+u_{yy} = 1 with BC: u|_{x^2+y^2=1} =0 ;

 

how to write down the command of the BC in solving this PDE?, btw can I make maple show me how to solve this PDE analytically?

 

Thanks in advance.

 

Here are the lines that I wrote so far:

pde := diff(u(x, y), x, x)+diff(u(x, y), y, y) = 1;

ans := pdsolve(pde)

 

how to add the BC correctly to pdsolve? I am not sure how to write the condition x^2+y^2=1 and that u will get a value on this boundary.

 

I read in the net that the method used in pdsolve numeric is the theta method, my question: is it the most efficient with regard to rate of convergence of the numerical solution of the PDE?

If not then why is it used as the default method?

 

Thanks.

 

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