This may be more of a MATLAB question, and if so, I do apologize for posting this in the wrong place.(adsbygoogle = window.adsbygoogle || []).push({});

I am doing a project on the Buttke scheme, which is a numerical approximation to the Biot-Savart Law. I am almost finished, but I am having trouble writing the code.

The scheme is Crank-Nicolson but it involves a cross product.

Here is the PDE:

$\displaystyle{\frac{\partial \mathbf{X}}(s,t){\partial t} = \textbf{X}(s,t) \times \frac{\partial ^2 \mathbf{X}(s,t)}{\partial s^2}}$

Here is the iteration:

$\displaystyle{\Big(\mathbf{X}_j^{n+1} - \mathbf{X}_j^{n}\Big) = \frac{\Delta t}{4(\Delta s)^2}\Big(\mathbf{X}_j^{n+1} + \mathbf{X}_j^{n}\Big) \times \Big(\mathbf{X}_{i+1}^{n} + \mathbf{X}_{i-1}^{n}+ \mathbf{X}_{i+1}^{n+1} + \mathbf{X}_{i-1}^{n+1} \Big)}$

If anyone could give me a hint about how to begin this iteration within a loop, that would be extremely helpful. I have done iterations before, but for some reason the cross product is really throwing me off.

Here is what I have (using the fact that in R2 cross products are really determinants)

r = dt/4*ds^2;

%Calculate Iterative Sequence

for j = 2:dt

for k = 1:tmax

A(k,j) = X(k+1,j)+X(k,j)

B(k,j) = X(k+1,j-1)+X(k,j-1)+X(k+1,j+1)+X(k,j+1)

Y(k+2,j) = X(k,j)+r*det(A,B);

end

end

I really don't need someone to write anything for me, just give me some guidance as to how this could be iterated. I feel like I am missing something simple.

Thanks so much,

Quakerbrat

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# PDE Iteration with cross product

Loading...

Similar Threads for Iteration cross product |
---|

I Cross product? |

**Physics Forums | Science Articles, Homework Help, Discussion**