Subject: Applying Boundary Conditions at Infinity?
From: Dan
Date: Sun, 13 Feb 2011 22:39:16 +0000 (GMT)
On Sun, 30 Jan 2011, Chris Nassar wrote:
> I'm trying to solve the differential equation A*p''(x)-p(x)/B=0 with the
> boundary conditions that p(infinity)=0 and p(xn)=pn.
> Maxima easily finds the general solution.
> ode2(A*'diff(p,x,2)-p/B,p,x);
> Is A B positive or negative?
> p
> x x
> --------------- - ---------------
> sqrt(A) sqrt(B) sqrt(A) sqrt(B)
> (%o1) p = %k1 %e + %k2 %e
> Applying the boundary conditions does not give the expected result
> bc2(%o1,x=inf,p=0,x=xn,p=pn);
> Maxima treats infinity as just another variable. Can I make maxima figure
> out that for p(infinity)=0 %k1 must be 0? Since I know the answer I can
> just set %k1 to zero, but it does not seem like a satisfactory solution.
> I couldn't find anything in the manual about it.
> Any help would be appreciated.
No other takers? Have you considered a change of independent variable
to something like u = 1-exp(xn-x) , to map the problem onto a finite
domain?
Now a question of my own: could one do something equivalent to this if
the homogeneous far-field condition were on the first derivative of p,
rather than on p itself?
--
HTH, and thanks,
Dan