Solving PDEs with IC, BCs: Help from Kevin

  • Thread starter Thread starter jimmygriffey
  • Start date Start date
  • Tags Tags
    Pde
jimmygriffey
Messages
4
Reaction score
0
Hi:

I have the following PDE:

ytzz=yzzzz+delta(t)

With I.C.: t=0, y=0; and B.C.s: z=0, y=0,yzz=0; z=-x,y=0,yz=0

Can someone show me how to solve it?

Kevin
 
Physics news on Phys.org
Yes, it is δ(t). The one is very similar to the previous one. After taking Laplace transform in t, this one will become the previous one. If I use the method pointed by other people, I have hard time to convert back (inverse Laplace transform) to time domain. That's why I ask the question again.

Kevin
 
jimmygriffey said:
Yes, it is δ(t). The one is very similar to the previous one. After taking Laplace transform in t, this one will become the previous one. If I use the method pointed by other people, I have hard time to convert back (inverse Laplace transform) to time domain. That's why I ask the question again.

Kevin
Yes - if one uses the Laplace Transform (which takes an equation from time domain to frequncy domain) then I believe it is the same problem. I'm expecting the problem is separable, i.e. Y(z,t) = Z(z)T(t). See if that works.
 

Thread 'Volterra equation of the second kind'

There is the following linear Volterra equation of the second kind $$ y(x)+\int_{0}^{x} K(x-s) y(s)\,{\rm d}s = 1 $$ with kernel $$ K(x-s) = 1 - 4 \sum_{n=1}^{\infty} \dfrac{1}{\lambda_n^2} e^{-\beta \lambda_n^2 (x-s)} $$ where $y(0)=1$, $\beta>0$ and $\lambda_n$ is the $n$-th positive root of the equation $J_0(x)=0$ (here $n$ is a natural number that numbers these positive roots in the order of increasing their values), $J_0(x)$ is the Bessel function of the first kind of zero order. I...
View full post »

Thread 'Visual Representation of Separation of Varables'

Are there any good visualization tutorials, written or video, that show graphically how separation of variables works? I particularly have the time-independent Schrodinger Equation in mind. There are hundreds of demonstrations out there which essentially distill to copies of one another. However I am trying to visualize in my mind how this process looks graphically - for example plotting t on one axis and x on the other for f(x,t). I have seen other good visual representations of...
View full post »

Similar threads

I Poisson's inhomogeneous PDE and its solutions
Replies
13
Views
3K
I Stuck on solving a non homogenous (linear) PDE
Replies
36
Views
4K
I Maxwell's equations PDE interdependence and solutions
Replies
5
Views
2K
I Why Lagrange’s method of solving Pp + Qq=R works?
Replies
3
Views
680
A Generic Solution of a Coupled System of 2nd Order PDEs
Replies
2
Views
2K
I 1D time dependent PDE - using orthogonal collocation
Replies
2
Views
3K
I Numerically solving a non-local PDE
Replies
3
Views
3K
A How to solve simple 2D space-time PDE numerically
Replies
5
Views
3K
I Heat Equation: Solve with Non-Homogeneous Boundary Conditions
Replies
4
Views
3K
I Understanding the change of variables for PDEs
Replies
2
Views
3K

Hot Threads

Recent Insights

Back
Top