Help with numerical methods assignment on Integration Using Matlab
The numerical methods assignment helper was tasked with integrating the equation:
Assistance with numerical methods homework on Using the Euler scheme.
In this equation,
– is the density field,
– is the chemical potential, and the Laplace operator for 2D case rewrites in the following way:
To find this differentiation, the numerical method homework helper used a second-order central difference scheme in the way:
the next relation was used:
Where for calculation
the scheme (3) was used.
So, for the Euler scheme we have:
Online numerical methods tutors getting the finite-differences
In the finite-difference scheme, the online numerical methods tutor used the periodic boundary conditions and the next values for constants and parameters:
For the level curve superimposed to a contour plot of the concentration field and to a vector plot of the gradient of the density field and for the values
and Helmholtz energy
We got the next results (contour plots presented only for some values of t)
Also, in this project, we calculated the radial distribution function of the Fourier transform
of the density field as:
And beneath some results at different times are presented.
These results gave us the possibility to calculate the average size of drops as:
In the final part of the project we repeated the above calculations for some different initial densities, these results gave us the possibility to compare the average size as a function of time for initial densities in the following way: