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

AI Thread Summary
The discussion focuses on finding the inverse Laplace transform of the functions exp(sqrt(1+s)) and sqrt(1+s). The original poster, drdolittle, reports difficulties using MATLAB and Mathematica, questioning whether a closed-form solution exists or if numerical techniques are necessary. Suggestions include using a Taylor series expansion for sqrt(1+s) and considering asymptotic expansions, but concerns about truncation and efficiency are raised. The poster is currently using Haar wavelet matrices for numerical techniques but is uncertain about their accuracy. The conversation emphasizes the challenges of obtaining a solution and the potential need for advanced numerical methods.
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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