Subject: Applying Boundary Conditions at Infinity?
From: Barton Willis
Date: Sun, 13 Feb 2011 17:02:14 -0600
-----maxima-bounces at math.utexas.edu 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.
I don't know anything about how bc2 works--maybe it a boundary at infinity is
outside its ability. Maybe this works:
--> ode2(A*'diff(p,x,2)-p/B,p,x);
"Is "A*B" positive or negative?"pos;
(%o35) p=%k1*%e^(x/(sqrt(A)*sqrt(B)))+%k2*%e^(-x/(sqrt(A)*sqrt(B)))
(%i36) sol : bc2(%,x=xxx,p=0,x=xn,p=pn);
(%o36) p=(pn*%e^((2*xxx)/(sqrt(A)*sqrt(B))+xn/(sqrt(A)*sqrt(B))-x/(sqrt(A)*sqrt(B))))/(%e^((2*xxx)/(sqrt(A)*sqrt(B)))-%e^((2*xn)/(sqrt(A)*sqrt(B))))-(pn*%e^(xn/(sqrt(A)*sqrt(B))+x/(sqrt(A)*sqrt(B))))/(%e^((2*xxx)/(sqrt(A)*sqrt(B)))-%e^((2*xn)/(sqrt(A)*sqrt(B))))
(%i38) lhs(sol) = gruntz(rhs(sol),xxx,inf);
(%o38) p=pn*%e^(xn/(sqrt(A)*sqrt(B))-x/(sqrt(A)*sqrt(B)))
Replacing gruntz with limit or tlimit fails, I think.
--Barton