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Numerical Inversion of Laplace Transform

Arnaud Mallet
Organization: University of Mauritius
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Many applied Maths/Physics subjects involve partial differential equations that may be solved by using Laplace transforms. However the inversion of the expressions in the transform domain is sometimes a formidable task or even impossible and hence a numerical inversion technique may be employed to obtain an approximate solution. It is very common to use Fourier and Hankel transforms in conjuncture with Laplace transforms in some PDE's. The Fourier/Hankel transform gets rid of the spatial dependency, while the Laplace transform removes the temporal dependence. The package NumericalInversion provides five inversion methods to invert Laplace transforms, Joint Fourier/Hankel-Laplace transforms. The inversion techniques are due to Durbin,Stehfest,Weeks,Piessens and Crump.

The package MultiVariable extends the package NumericalInversion whenever functions of several variables have to be inverted. The package Errors provides error measurements that assess the power of the numerical inversion schemes.

*Applied Mathematics > Numerical Methods
*Mathematics > Calculus and Analysis > Differential Equations

Numerical Inversion of Laplace transforms, Joint Fourier, Laplace transforms, Joint Fourier Laplace transforms
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Errors.m (18.8 KB) - Mathematica package
MultiVariable.m (66.3 KB) - Mathematica package
NumericalInversion.m (72.3 KB) - Mathematica package