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Re: Numerical inversion of the Laplace Transform: Potential ilaplace may
From: |
Stephen Montgomery-Smith |
Subject: |
Re: Numerical inversion of the Laplace Transform: Potential ilaplace maybe? |
Date: |
Mon, 04 Feb 2013 06:58:16 -0600 |
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Mozilla/5.0 (X11; Linux i686; rv:17.0) Gecko/20130106 Thunderbird/17.0.2 |
On 02/04/2013 05:13 AM, Robert Durkacz wrote:
> On Sun, Feb 3, 2013 at 7:26 AM, Fernando <address@hidden> wrote:
>
>> See attached a algorithm for computing the inversion of the Laplace
>> Transform, algorithm developed by my thesis supervisor JAC Weideman back in
>> the day and co authored by N. Trefethen. The user must still choose the
>> number of functions evaluations. Maybe someone can do some error truncation
>> to avoid manual selection of function evaluations.
>
> I looked at the code and understood enough to know that the question I
> have is a little off-topic but I will ask it anyway. Suppose I have
> numerically evaluated the Laplace transform of some function of t and
> therefore have a big table of the transform for real values s. How can
> I invert this numerically? (Not by using any form of contour
> integration as Fernando's algorithm does, I think because this will
> ask for complex values of s.)
I asked about this many years ago on newsgroups like sci.math.research.
I was told that it was a very ill-conditioned problem, in that a very
small numerical change to the Laplace Transform would probably result in
a huge change in the value of the function.
I was quite excited when I saw the heading "numerical inversion of
Laplace Transform," and I expected that someone had figured out a good
solution to the problem. But then I looked at the code and saw that it
evaluated the function at complex values.
Re: Numerical inversion of the Laplace Transform: Potential ilaplace maybe?, Robert Durkacz, 2013/02/04
- Re: Numerical inversion of the Laplace Transform: Potential ilaplace maybe?,
Stephen Montgomery-Smith <=