Inverse Laplace transform

In summary, the conversation is about finding the inverse Laplace transform of two functions - exp(sqrt(1+s)) and sqrt(1+s). The person has tried using MATLAB and Mathematica but was unable to get a result. They are wondering if there is a closed form solution or if they need to use a numerical technique. One person suggests using a Taylor series, while another suggests using an asymptotic expansion. The person is currently using a numerical technique with Haar wavelet matrices but is unsure about its accuracy and efficiency. They are seeking help and suggestions to solve this problem.
  • #1
drdolittle
27
0
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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  • #2
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
 
  • #3
That's a tough one! Would an asymptotic expansion be of any use?
 
  • #4
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
 

1. What is the Inverse Laplace Transform?

The Inverse Laplace Transform is a mathematical operation that allows us to find the original function, given its Laplace transform. It is the reverse process of the Laplace Transform, which transforms a function from the time domain to the frequency domain.

2. How is the Inverse Laplace Transform calculated?

The Inverse Laplace Transform is typically calculated using a table of known transforms, partial fraction decomposition, or the residue theorem. It involves finding the coefficients of the polynomial expressions and using the inverse transform formula to obtain the original function.

3. What is the significance of the Inverse Laplace Transform in engineering?

The Inverse Laplace Transform is an essential tool in solving differential equations in engineering. It allows engineers to model and analyze dynamic systems, such as electrical circuits and control systems, in the frequency domain, which can be more convenient and efficient than working in the time domain.

4. What are the properties of the Inverse Laplace Transform?

The Inverse Laplace Transform has several properties that make it a powerful tool for solving differential equations. These properties include linearity, time shifting, scaling, differentiation, integration, and convolution.

5. How is the Inverse Laplace Transform used in real-world applications?

The Inverse Laplace Transform has numerous applications in various fields, such as electrical engineering, control systems, signal processing, and physics. It is used to model and analyze complex systems, including circuits, filters, and mechanical systems, in the frequency domain.

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