How Can I Find the Inverse Laplace Transform of These Functions?

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Discussion Overview

The discussion revolves around finding the inverse Laplace transform of specific functions, namely exp(sqrt(1+s)) and sqrt(1+s). Participants explore whether these functions have closed form solutions or if numerical techniques are necessary for their evaluation.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant expresses difficulty in finding the inverse Laplace transform of the functions using MATLAB and Mathematica, questioning the existence of closed form solutions versus the need for numerical techniques.
  • Another participant suggests using the Taylor series expansion of sqrt(1+s) to express the inverse Laplace transform as an infinite sum.
  • A different participant proposes the idea of using an asymptotic expansion as a potential method for tackling the problem.
  • The original poster responds to the Taylor series suggestion, expressing concerns about truncation and its efficiency compared to numerical techniques.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the best approach to find the inverse Laplace transform, with multiple competing views on the utility of series expansions versus numerical methods remaining unresolved.

Contextual Notes

There are limitations regarding the assumptions made about the functions and the potential accuracy of the proposed numerical techniques, as well as the implications of truncating the Taylor series.

drdolittle
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Can somebody help me to find the inverse laplace transform of these functions

exp(sqrt(1+s))
sqrt(1+s))

I tried solving these using MATLAB and mathematica,it is unable to give a result.
Do they contain any closed form solution or should i have to go for a numerical technique to solve them?If so,anybody aware of accurate and efficient numerical technique?
Currently iam using a Numerical technique using Haar wavelet matrices but doubt on its validity in terms of both accuracy and efficiency.
sombeody please help me.Thanx in advance

regards
drdolittle

:cry:
 
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Try replacing sqrt(1+s) by it Taylor series, 1+x/2 -(x^2)/8 +(x^3)/16 +...
then express the inverse Laplace transform as an infinite sum.

Ray
 
That's a tough one! Would an asymptotic expansion be of any use?
 
thanx for the suggestion.
but if we use a taylor series we have to truncate at some point of time and i presume it will not be more efficient than numerical techniques...i hope so

Regards
drdolittle
 

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