Comparing Four Methods of Numerical Inversion of Laplace Transforms (NILT)
This Demonstration compares the efficiency of four methods for numerical inversion of Laplace transforms (NILT). The algorithms employed refer mainly to [1–3].[more]
The inverse Laplace transform of the selected function (with Laplace variable ) can be approximated numerically (shown as dots) using the selected NILT method. The closed-form expression of inverse Laplace transform is plotted as a full line.
Numerical inversion can be performed in double precision or using the multi-precision computing mode of Mathematica.[less]
Numerical inversion of Laplace transforms (NILT) has become increasingly important in many application fields.
Four NILT methods are compared in this Demonstration, with special regard to some features of Laplace transformed functions, the time interval considered , the number of computation nodes in relation to the parameter , and the computing mode (double precision or multi-precision).
The inverse Laplace transform of the selected function (with Laplace variable ) can be approximated numerically (shown as dots) using the selected NILT method together with the relevant algorithm. The exact inverse Laplace transform is plotted as a full line. In some cases of very bad accuracy, computed data (dots) may stay outside the top graph.
sets the number of Laplace transform values required for evaluation of one value, which is for the Gaver–Stehfest and Gaver–Wynn's rho methods, for the Fourier–Euler method, and for the "fixed" Talbot method.
Numerical inversion can be performed in double-precision or multi-precision computation mode; is the relative error.
The output accuracy is . The number of significant digits is the integer part of accuracy. Note that the input precision automatically switches to the multi-precision computing mode for Gaver–Wynn's rho algorithm because of its instability in double precision.