Hb

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7 years, 166 days

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These are questions asked by Hb

Hi,

I have been trying to solve 2D Diffusion Equation with zero Neumann BC over the unit disk. If I use Gaussian type function with a sharp peak as initial condition, I get huge errors between initial values. Let's say u(r,phi,t) is the solution of the PDE and f(r,phi) is initial value function. The expectation is for the point (r*,phi*) ,  u(r*,phi*,0)=f(r*,phi*), but it is not.

Is Numerical integration in Maple not able to handle such sharp peak? I tried some of the built-in methods such as MonteCarlo,CubaVegas but no difference.

It might be a good idea to specify some nodes arround the peak. There is a command called "peaks", but I could not use it, error message says "invalid arguments".

Thanks in advance.

Soln_2D_Gaussian.mw

Hello,

I have been trying to compute the analytical solution of two dimensional diffusion equation with zero neumann boundary conditions (no-flux) in polar coordinates using the solution in Andrei Polyanin's book. When I use 2d Gaussian function as initial condition, i cannot get the result. If I use some nicer function like f(r,phi)=1-r; there is no problem.  

Any idea why this happens? or any suggestion to compute the analytical solution?

Thanks!

HB 

M := Matrix([[3.83170597020751, 7.01558666981561, 10.1734681350627, 13.3236919363142, 16.4706300508776], [1.84118378134065, 5.33144277352503, 8.53631636634628, 11.7060049025920, 14.8635886339090], [3.05423692822714, 6.70613319415845, 9.96946782308759, 13.1703708560161, 16.3475223183217], [4.20118894121052, 8.01523659837595, 11.3459243107430, 14.5858482861670, 17.7887478660664], [5.31755312608399, 9.28239628524161, 12.6819084426388, 15.9641070377315, 19.1960288000489], [6.41561637570024, 10.5198608737723, 13.9871886301403, 17.3128424878846, 20.5755145213868], [7.50126614468414, 11.7349359530427, 15.2681814610978, 18.6374430096662, 21.9317150178022], [8.57783648971407, 12.9323862370895, 16.5293658843669, 19.9418533665273, 23.2680529264575], [9.64742165199721, 14.1155189078946, 17.7740123669152, 21.2290626228531, 24.5871974863176], [10.7114339706999, 15.2867376673329, 19.0045935379460, 22.5013987267772, 25.8912772768391], [11.7708766749555, 16.4478527484865, 20.2230314126817, 23.7607158603274, 27.1820215271905]]):

c := 10:

A := 5:

w := proc (r, phi, t) options operator, arrow; int(int(f(xi, eta)*G(r, phi, xi, eta, t)*xi, xi = 0 .. 5), eta = 0 .. 2*Pi) end proc:

with(plots):

Warning,  computation interrupted

 

``



Download 2d_soln.mw

Hello;

I would like to extract data from a 2D plot to compare my numerical result in Matlab. 

I used this command.

However, I need to spesify the nodes on x axis to get the error in Matlab. My matlab codes give the result as fix step size i.e [0 0.1 0.2 ... 1.0] or [0 0.01 0.02 ... 1.00] etc.

Is there any command in Maple to spesify the nodes on x axis?

Thanks you!

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