MaplePrimes - answers and comments on Question, Variation to the Helmholtz equation???

pdsolve

Robert Israel — Thu, 18 Nov 2010 13:30:17 Z

I tried it with pdsolve, but Maple couldn't solve it ina reasonable time (one try got a memory allocation error, another I stopped with Time 4954 seconds and Bytes 1.35G). This could indicate a bug, or perhaps it's just a very complicated solution.

with(VectorCalculus); SetCoordinates(cartesian[x,y,z]);
F:= VectorField(<f1(x,y,z),f2(x,y,z),f3(x,y,z)>);
eq:= Laplacian(F) + 2*b*c*Curl(F) + c*F;
pdsolve(convert(eq,set));

However, you might look for solutions of the following form:

F = <a1,a2,a3>*exp(k*x)

(and those obtained by symmetry from that, and linear combinations...)

Functions of x

Robert Israel — Sun, 21 Nov 2010 12:21:24 Z

Here are the solutions that are functions of x alone.

> with(VectorCalculus); SetCoordinates(cartesian[x,y,z]);
  F:= VectorField(<f1(x),f2(x),f3(x)>);
  eq:= Laplacian(F) + 2*b*c*Curl(F) + c*F;
  dsolve(convert(eq,set));

Robert thanks, I am just getting back to this problem & I think what you replied might help

tsunamiBTP — Tue, 07 Dec 2010 21:29:21 Z

Robert thanks, I am just getting back to this problem & I think what you replied might help