An algorithm for the inversion of Laplace transforms using Puiseux expansions

作者：Wang, Tongke^*; Gu, Yuesheng; Zhang, Zhiyue

来源：Numerical Algorithms, 2018, 78(1): 107-132.

DOI：10.1007/s11075-017-0369-y

• Inverse Laplace transform
• Bromwich integral
• Puiseux expansion
• Gauss-Legendre rule
• Gauss-Kronrod rule
• Error estimate

This paper is devoted to designing a practical algorithm to invert the Laplace transform by assuming that the transform possesses the Puiseux expansion at infinity. First, the general asymptotic expansion of the inverse function at zero is derived, which can be used to approximate the inverse function when the variable is small. Second, an inversion algorithm is formulated by splitting the Bromwich integral into two parts. One is the main weakly oscillatory part, which is evaluated by a composite Gauss-Legendre rule and its Kronrod extension, and the other is the remaining strongly oscillatory part, which is integrated analytically using the Puiseux expansion of the transform at infinity. Finally, some typical tests show that the algorithm can be used to invert a wide range of Laplace transforms automatically with high accuracy and the output error estimator matches well with the true error.

• 出版日期2018-5
• 单位南京师范大学; 天津师范大学; 河南科技学院