Numerical Inversion of 3D Laplace Transforms for Weakly Nonlinear Systems Solution

The paper deals with a technique for numerical inversion of three-dimensional Laplace transforms (3D NILT) being based on the FFT & IFFT in conjunction with the quotient-dffference algorithm. This method generalizes 2D NILT technique developed formerly to three variables. Especially an error analysis has resulted in a new formula equating a relative error of the method to paths of the integration of triple Bromwich integral. To evaluate triple infinite sums obtained by numerical integration, the partial inversion technique is used. The method was algorithmized in Matlab language environment and applied for solving a response of a weakly nonlinear circuit via Volterra series expansion to demonstrate its practical usefulness.