Finding Solutions to a PDE System with Known Scalar Function

vibe3
Messages
39
Reaction score
1
Hi all, I am looking for ways to solve the following system of equations for \vec{B}:
<br /> \vec{B} \cdot \nabla f = 0<br />
<br /> \left( \nabla \times \vec{B} \right) \cdot \nabla f = 0<br />
<br /> \nabla \cdot \vec{B} = 0<br />
and f is a known scalar function. I think we can assume there is a solution since we have 3 equations and 3 unknown components of \vec{B}.

I don't think there is an analytic solution here, but could someone give some pointers on how one would solve this system numerically?
 
Physics news on Phys.org
Method of characteristics I think?
 
Thread 'Direction Fields and Isoclines'
I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...

Similar threads

Back
Top