Inverse Laplace transform with p^-1 and exponential

kewei chen
Messages
2
Reaction score
0
Hello everyone, I have spend whole day but still not figure out an inverse Laplace transform. Hope someone can help me. The question is in the attachment. I'm trying to extract u^2/4D^2 out the bracket to match the standard inverse table, but it seems difficult to deal with the square root. Thanks and appreciate.
 

Attachments

  • question.jpg
    question.jpg
    19.5 KB · Views: 849
  • table.jpg
    table.jpg
    41.4 KB · Views: 10,620
Physics news on Phys.org
Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 
Greg Bernhardt said:
Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
I don't know how the author did the inverse transform. It seems numerical inversion is the only way I can use.
 

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 Solving PDE with Laplace Transforms & Inverse Lookup
Replies
1
Views
2K
Inverse Laplace Transform of a product of exponential functions
Replies
1
Views
4K
What is the Inverse Laplace Transform of e^(-sx^2/2)?
Replies
10
Views
2K
I PDEs: Laplace's Equation over a Parallelogram
Replies
10
Views
3K
Why is the heaviside function in the inverse Laplace transform of 1?
Replies
8
Views
4K
Inverse laplace transform for unique diffusion type problem
Replies
3
Views
4K
What is the inverse Laplace transform of F(s)?
Replies
1
Views
2K
MHB What is the Inverse Laplace Transform of 2s+7-e^-2s/(s+1)^2?
Replies
3
Views
2K
Inverse Laplace transform with unit step function
Replies
3
Views
5K
Taking the inverse laplace of this?
Replies
3
Views
3K

Hot Threads

Recent Insights

Back
Top