Problem computing inverse Laplace transform of the Bessel function
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Kevin B
el 11 de Nov. de 2017
Respondida: BeeTiaw
el 5 de Ag. de 2020
I am trying to evaluate the inverse Laplace transform of a function that includes the modified Bessel function of the second kind, i.e., my function is f_s = sqrt(a*s)*besselk(1,2*sqrt(a*s)), where a is a constant (say a = 0.5) and 's' is defined as a symbol. To evaluate the inverse Laplace transform of this function, I used the built-in Matlab function 'ilaplace' as transV = ilaplace(f_s,s,t), where I want to evaluate my function at 't' = 2. However, the problem I am getting is that the inverse transformed expression transV still contains 's' variable, which I supposed to transform to 't' after the inverse Laplace transform.
Can anyone help me with what is the problem with this approach? I checked the Matlab documentation and still couldn't figure out the solution. I already tried using 'vpa' function as it was suggested in one of the Matlab forums, but that didn't help to get rid of 's'. I am stuck with this and would really appreciate any help on it.
My code is
a = 0.5; t = 2;
syms s;
f_s = 1/s*sqrt(a*s)*besselk(1,2*sqrt(a*s));
transV = ilaplace(f_s,t); % or transV = vpa(ilaplace(f_s,t));
With this, the final result transV still has an expression which is a function of 's' although it should be transformed after ilaplace.
2 comentarios
David Goodmanson
el 11 de Nov. de 2017
Hi Kevin,
It appears that the result is just a slightly different inverse laplace transform that the toolbox can't do either. Might not exist in closed form.
Respuesta aceptada
Walter Roberson
el 11 de Nov. de 2017
Maple says that for a > 0, the result is (1/2)*exp(-a/t)
3 comentarios
Walter Roberson
el 11 de Nov. de 2017
Under the assumption that a1, a2, a3, a4, s are all > 0, then
(1/2)*(BesselK(1, 2*a2^(1/2)*a3^(1/2)/t)*exp((-a3-a2)/t)*a2^(1/2)*a3^(1/2)+BesselK(1, 2*a1^(1/2)*a4^(1/2)/t)*exp((-a4-a1)/t)*a4^(1/2)*a1^(1/2)+BesselK(1, 2*a2^(1/2)*a4^(1/2)/t)*exp((-a4-a2)/t)*a4^(1/2)*a2^(1/2)+BesselK(1, 2*a1^(1/2)*a3^(1/2)/t)*exp((-a3-a1)/t)*a1^(1/2)*a3^(1/2))/t
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BeeTiaw
el 5 de Ag. de 2020
Can you look at my problem in here please? https://uk.mathworks.com/matlabcentral/answers/575788-stehfest-algorithm-for-a-problem-of-inverse-laplace-with-bessel-function
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