Help me find f(r) in this equation

[BAT_MAN]

Can anybody find f(r) when

Δf(r)=0 or (del.del)f(r)=0

 

[Dmitrij]

Re: find f(r)

The answer to your question depends on what Δ is. I think you meant Laplace operator. Also it's very important in what coordinate system the function is given

1) if it's Dekart coordinate system then the equation Δf(r)=0 is a famous Laplace equation, and Laplacian is identical to the sum of private derivatives of the second order:

Δf(r) = d^2(f(r))/dr - second derivative.

Theequation turn out to be differential equation (linear) of 2nd order. The solution is linear function with 2 constants:

f = C1*r + C2, where C1,C2 - constants. In order to find these constants you should study initial conditions.

2) If r means, that we are working in spherical coordinate system, the the expression for Laplacian is complicated. It may be found according to the definition:

Δf(r) = div(grad r). Also you should revise Lame coefficients.

After this you need to solve the corresponding differential equation.

With respect,

Dmitrij

 

[mudrik]

Re: find f(r)

Nabla f = 0 is a very famous operation in mathematical physics.

You can solve the equation analytically, if you restrict
the problem in orthogonal coordinate systems
(i.e. rectangular, cylindrical, spherical, elliptical, etc.)
otherwise you should take numerical approach (finite difference,
finite element or others).
If you are talking about electromagnetics, the books
Fields and Waves in Electromagnetics by D.K. Cheng and
Numerical Electromagnetics by M. Sadiku
can give you quantitative and qualitative informations

regards