## 24 Reputation

15 years, 115 days

## MaplePrimes Activity

### These are replies submitted by griffgruff

On inspection, it appears that the first code example can be simplified to:

V:=Del(u(x,y));
n:=Normalize(V,2);
bcN := simplify(DotProduct(n,V));

## Further clarification...

@Rouben Rostamian  Thank you for your replies.

The function u(x,y) is the solution to a PDE (elliptical) which represents a 2D surface over its domain. The point (xo,yo) lies on the bounday of the domain. I wish to calculate the Neumann boundary condition (the normal derivative) at (xo,yo), i.e. du/dnn . del(u) . I may have confused the issue by showing u in 'bold'. Actually, u is a scalar function not a vector function.

The boundary does not need to be a level curve (although it can be); for example, the solution to a well posed Laplace equation with a Dirichlet boundary whose value varies over its length. This could represent (at equilibrium) the Heat equation with different temperatures imposed along the boundary.

## Clarification...

@Rouben Rostamian  Just to clarify, n and u are related. If u(x,y) represents a 2D surface and n the unit normal at point (xo,yo) on the boundary, then

n . del(u)

represents the Neumann boundary condition for a PDE with solution u(x,y) at point (xo,yo).

Apologies for any confusion.

## pdsolve - query...

Sorry for any confusion due to the spelling mistake in the subject heading.

## Problem solved...

Thanks very much. Your suggestion works fine. Regards, Graham

## Problem solved...

Thanks very much. Your suggestion works fine. Regards, Graham
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