Adaptive inversion method for the Laplace integral transform

To expand its area of application as well as improve the accuracy of the results of numerical inversion using the Laplace integral transform inversion, a more exact adaptive method for the numerical integral was employed. First, by means of the Euler identity, from complex function theory, the inversion integral in complex domain was simplified into a general integral with real variables and an infinite interval. Then, a truncation error was introduced and the inversion integral was calculated in a special finite interval numerically using an adaptive trapezium integral method with a set calculation error. The inversion results indicated that this adaptive method is very accurate at all continuous points except for some special points, for example infinite and jump points. The theory of this method is simple, and errors can be controlled more easily.