Convergence problems and optimal parameter estimation in FFT-based method of numerical inversion of two-dimensional Laplace transforms

When solving certain partial differential equations, namely those describing transient behaviour of linear dynamical systems, Laplace transforms in two variables can very be useful. However, it is often either too difficult or impossible to get their objects by analytic method. There were developed a few methods that enable finding the objects numerically. One of them is the FFT-based method recently published and verified using Matlab language. Its main advantage lies in high speed of computation, however, a proper technique of convergence acceleration has to be applied to achieve required accuracy. It was shown either the epsilon or quotient-difference algorithms are convenient for this purpose. In this paper, the error analysis and the estimation of optimal parameters for the FFT-based 2D-NILT in conjunction with quotient-difference algorithm are newly carried out.