Numerical inversion of 2-D Laplace transforms by fast Hartley transform computations

Laplace transforms in two variables are useful in the solution of partial differential equations. However, their analytic inverses are often difficult to obtain. In this paper, the numerical method based on evaluating the Bromwich integral and using the computation algorithm of fast Fourier transform (FFT) is extended to the inversion of two-dimensional (2-D) Laplace transforms. A new inversion formula is devised so that the values of the inverted 2-variable function on the rectangle grids can be efficiently obtained via multiple sets of 2-D fast Hartley transform (FHT) computations. The proposed FHT-based inversion algorithm is thus suitable for the computation in a multiprocessor environment.