Abstract
In this paper, new algorithms are proposed for Fredholm integral equations of the first kind corresponding to the inverse Laplace transform. We apply high order numerical quadratures to the truncated integral equation and apply regularization to the discretized linear systems. The resulted regularized least square problems are then solved by the reduced QR factorization method. Several examples taken from the literature are tested. Numerical results show that the approximate inverse Laplace transform obtained by our approach can be very accurate.
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Communicated by Yuesheng Xu and Hongqi Yang.
The research was supported in part by the Guangdong Provincial NSF under contract no. 10151503101000023.
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Lin, FR., Liang, F. Application of high order numerical quadratures to numerical inversion of the Laplace transform. Adv Comput Math 36, 267–278 (2012). https://doi.org/10.1007/s10444-011-9202-7
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DOI: https://doi.org/10.1007/s10444-011-9202-7