Technique of 3D NILT based on complex Fourier series and quotient-difference algorithm

The paper deals with a technique of the numerical inversion of three-dimensional Laplace transforms (3D NILT) based on a complex Fourier series approximation, in conjunction with a quotient-difference (q-d) algorithm. It is a generalization of a 2D NILT technique of the same principle to three variables. Especially, a detailed error analysis is done resulting in a formula giving a connection between a relative error and the paths of a numerical integration of a triple Bromwich integral. To evaluate triple infinite sums gained by the numerical integration, a partial inversion technique is applied while utilizing the FFT and IFFT algorithms for the fast evaluation, and the q-d algorithm to speed up the convergence of residual infinite series. The technique was algorithmized in a Matlab language and experimentally verified.