Improved method of numerical inversion of two-dimensional Laplace transforms for dynamical systems simulation

摘要

Laplace transforms in two variables can very be useful in the solution of partial differential equations describing transient behaviour of linear dynamical systems. It is often either too difficult or even impossible to obtain their originals analytically, however. The paper presents a novel way of the numerical inversion of two-dimensional Laplace transforms (2D-NILT). The method comes Out the previous works where the 2D-NILT techniques based on the FFT and the ε-algorithm was elaborated. Here, however, quotient-difference algorithm of Rutishauser is used to accelerate the convergence of a two-dimensional complex Fourier series instead of the ε-algorithm. This leads to an improvement in the numerical stability of the method while the accuracy is approximatelly the same.