Accuracy improvement of the FFT-based numerical inversion of Laplace transforms

Abstract

The authors present an improvement on the FFT-based numerical inversion of Laplace transforms. Since inversions obtained by the FFT-based method contain large errors, especially for the latter half of the computed region, only the former half is acceptable. The truncation error, which is the greater part of the errors, is analysed and an acceleration method is proposed that uses a property of the complex frequency variable s. This acts as the differential operator in the time domain. The errors are significantly reduced by the proposed method, and thus the inversions become acceptable for almost the entire region.