I'm using Sage to check the initial condition for a solution to the advection-diffusion equation. Here the initial condition is checked using a limit whose result should be zero. But, Sage gives the difference of two equivalent exponentials and leaves it without simplifying to zero. These exponentials only differ in that one has a 1/10 in it and one has a 0.1.
Here is the code:
var('u,x,t') erfc(x) = 1-erf(x) k=0.03 D=0.3 C=2. u(x,t) = C*1/2*(erfc((x-k*t)/sqrt(4*D*t))+exp(x*k/D)*erfc((x+k*t)/sqrt(4*D*t))) assume(x>0) ans=limit(u(x,t),t=0,dir='+') print ans.simplify_full()
The result is:
-e^(1/10*x) + e^(0.1*x)
Any advice on how to get this to simplify to zero?