Recent content by masnet

Hello all, Just wanted to come and report that the problem doesn't seem to be solvable using the methods that you suggested and we discussed together. I've worked on couple of similar problems and whenever there's a function like U(0,t) hanging in the PDE (which is to be determined while...

Yes, this is correct. Where does this come from? I can't follow you on this. If you're referring to my earlier comment, then that was when n=0, i.e.: \lim_{t\rightarrow \infty} p_u(0;t) = 1 However, we can't use this fact to solve this PDE. I know this because I know what the...

Just jumped into comment on few things: U(0,t) = 0 Can't be true, considering the problem structure. U(0,t) is a Probability Generating Function. The inverse z-transform of U(0,t) is a time-dependent probability distribution and I know that it converges to 1 as t goes to infinity. Yes, N...

Just a quick note here that I mentioned the initial condition as u(z,0)=z^K in my first post and K there was a parameter defined in the original problem description. Later in a post, I mentioned that the initial condition is u(z,0)=z^{N-1}, to be more specific. N is a parameter and fixed. If you...

Thank you JJacquelin, Mute and jackmell for your comments. I greatly appreciate your time! Seems I need more time to think about and work on your proposals. I will post back once I conclude. Thank you very much again! :)

@JJacquelin Thank you very much for sharing your thoughts and I hope you've enjoyed your vacation! :) Now, off to the PDE: OK, now it seems in order for me to be able to respond to your comments, I should go back and explain where this PDE comes from. The original problem is a...

@Mute Thank you very much for your comment and the steps you've outlined. Seems I'm too tired to remember why this didn't work. I will think about it again and respond later on; maybe this time works! Thanks again! :)

OK, thanks anyway for your time! :)

@jackmell Thanks for your comment. Unfortunately, it doesn't seem to me that Separation of Variables can get me out of this gridlock. Following the original notation, if I take U(z,t)=Z(z)T(t) and assuming that K is the separation constant, I will end up like this: The ODE in t will result...

Hello again! @Eynstone The substitution that you suggested leads to the following equation: \frac{\partial V(z,t)}{\partial t}+(1-z)\frac{\partial V(z,t)}{\partial z}=(\frac{1}{z}-1)\left(V(z,t)-V(0,t)-z\right) I fail to see your point in suggesting this; this...

Hello! Thank you very much JJacquelin and Eynstone for your comments! I just received a notification about your replies; I will go through your proposals and will get back to you in few days to let you know if I managed to find a solution. Cheers! PS: In the meantime, I appreciate it if you...

Hello all! I appreciate it if you can share any thoughts that you may have regarding how to solve the following PDE: \frac{\partial U(z,t)}{\partial t}+(1-z)\frac{\partial U(z,t)}{\partial z}=(\frac{1}{z}-1)\left(U(z,t)-U(0,t)\right) Initial condition:U(z,0)=z^{K} U(0,t) arises due...