I'd like to solve a 1st order differential equation like this in 1d domain:
du/dx =u
x in [0,2]
u(0) = 1000
while I was using the General Form PDE in stationary , there are two boundary point in x=0 and x=2.
the default condition is zero flux condition at both ends. However, for a 1st order equation there should be only one boundary condition. zero flux at x = 2 is over-determinant for this problem.
The results obtained is also oscillating as shown in the attachment.
So, my question is: what condition should I impose at x=2? for this kind of equation?
du/dx =u
x in [0,2]
u(0) = 1000
while I was using the General Form PDE in stationary , there are two boundary point in x=0 and x=2.
the default condition is zero flux condition at both ends. However, for a 1st order equation there should be only one boundary condition. zero flux at x = 2 is over-determinant for this problem.
The results obtained is also oscillating as shown in the attachment.
So, my question is: what condition should I impose at x=2? for this kind of equation?