Items tagged with montecarlo

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

In a previous post, I promised to write about testing the quality of pseudo-random number sequences.  I'll post later about some of the statistical tests often used, but I first wanted to mention a sort of practical test one can do. One of the many things you might want to do with pseudorandomly generated numbers is Monte Carlo integration/simulatation/etc.  As mentioned by acer in this comment, Monte Carlo integration can be shown to work better with some of the pseudorandom number generators (PRNGs) which are considered inferior in a statistical sense.  In this post, we will play with a simple Monte Carlo approximation of π.

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