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Title says it all. How do I go about finding inverse Laplace transform of that expression? If it were complete exponents, I would have used partial fractions. But what to do with non integer exponents?

K. Rmth
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tumchaaditya
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  • Where did the expression come from? Did you perform a Laplace transform first, simplify and now need to do the inverse Laplace transform? – John Habert Feb 07 '14 at 18:29
  • @JohnHabert: I am solving coupled partial differential equations(space and time) with a complicated boundary conditions. So, I solved it in Laplace domain and now I am trying to invert the solution. – tumchaaditya Feb 08 '14 at 19:46

1 Answers1

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$$\frac{1}{s^2-As^{1.5}} = -\frac{1}{A^3(\sqrt{s}+A)} + \frac{1}{A^3\sqrt{s}}-\frac{1}{A^2s}+\frac{1}{As^{1.5}}$$

The inverse Laplace transform of the first term doesn't have a closed form solution:

http://www.wolframalpha.com/input/?i=inverse+Laplace+transform+1%2F%28sqrt%28s%29%2BA%29

The rest of the terms are easy.

Perry Elliott-Iverson
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  • erfc is considered a closed-form solution. Can you derive it yourself? – Ron Gordon Feb 07 '14 at 21:15
  • I suppose it depends on your definition of closed-form solution.

    http://math.stackexchange.com/questions/9199/what-does-closed-form-solution-usually-mean

     – Perry Elliott-Iverson Feb 07 '14 at 21:43
  • I have a specific definition that says an expression is "closed-form" when there exists algorithms that allow one to compute that expression significantly faster to within machine precision than via a numerical integration. For erf and erfc, this is absolutely the case. – Ron Gordon Feb 07 '14 at 21:52
  • Here is where I stated my definition of closed-form: http://math.stackexchange.com/questions/562769/what-would-qualify-as-a-valid-reason-to-believe-there-is-a-closed-form/562810#562810 – Ron Gordon Feb 07 '14 at 21:57