{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T18:36:23Z","timestamp":1778783783975,"version":"3.51.4"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2012,8,2]],"date-time":"2012-08-02T00:00:00Z","timestamp":1343865600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2013,6]]},"DOI":"10.1007\/s11075-012-9625-3","type":"journal-article","created":{"date-parts":[[2012,8,1]],"date-time":"2012-08-01T00:51:06Z","timestamp":1343782266000},"page":"339-355","source":"Crossref","is-referenced-by-count":155,"title":["Review of inverse Laplace transform algorithms for Laplace-space numerical approaches"],"prefix":"10.1007","volume":"63","author":[{"given":"Kristopher L.","family":"Kuhlman","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,8,2]]},"reference":[{"key":"9625_CR1","doi-asserted-by":"crossref","first-page":"979","DOI":"10.1002\/nme.995","volume":"60","author":"J Abate","year":"2004","unstructured":"Abate, J., Valk\u00f3, P.: Multi-precision Laplace transform inversion. Int. J. Numer. Methods Eng. 60, 979\u2013993 (2004). doi: 10.1002\/nme.995","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"3","key":"9625_CR2","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1080\/10652460108819314","volume":"11","author":"A Al-Shuaibi","year":"2001","unstructured":"Al-Shuaibi, A.: Inversion of the Laplace transform via Post-Widder formula. Integral Transforms Spec. Funct. 11(3), 225\u2013232 (2001). doi: 10.1080\/10652460108819314","journal-title":"Integral Transforms Spec. Funct."},{"key":"9625_CR3","volume-title":"Numerical Methods for Scientists and Engineers","author":"H Antia","year":"2002","unstructured":"Antia, H.: Numerical Methods for Scientists and Engineers, 2nd edn. Birkh\u00e4user, Cambridge, MA (2002)","edition":"2"},{"key":"9625_CR4","doi-asserted-by":"crossref","unstructured":"Bailey, D.H., Hida, Y., Li, X.S., Thompson, B.: ARPREC: An Arbitrary Precision Computation Package. Tech. Rep. LBNL-53651, Lawrence Berkley National Lab (2002)","DOI":"10.2172\/817634"},{"key":"9625_CR5","author":"M Bakker","year":"2011","unstructured":"Bakker, M., Kuhlman, K.: Computational issues and applications of line-elements to model subsurface flow governed by the modified Helmholtz equation. Adv. Water Resour. (2011). doi: 10.1016\/j.advwatres.2011.02.008","journal-title":"Adv. Water Resour."},{"key":"9625_CR6","doi-asserted-by":"crossref","first-page":"W01510, 12","DOI":"10.1029\/2011WR010955","volume":"48","author":"KS Barnhart","year":"2012","unstructured":"Barnhart, K.S., Illangasekare, T.H.: Automatic transport model data assimilation in Laplace space. Water Resour. Res. 48, W01510, 12 (2012). doi: 10.1029\/2011WR010955","journal-title":"Water Resour. Res."},{"key":"9625_CR7","volume-title":"Numerical Inversion of the Laplace Transform: Applications to Biology, Economics, Engineering, and Physics","author":"R Bellman","year":"1966","unstructured":"Bellman, R., Kalaba, R.E., Lockett, J.A.: Numerical Inversion of the Laplace Transform: Applications to Biology, Economics, Engineering, and Physics. Elsevier, Amsterdam, The Netherlands; New York (1966)"},{"key":"9625_CR8","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-48860-3","volume-title":"Boundary Element Techniques: Theory and Practice in Engineering","author":"C Brebbia","year":"1984","unstructured":"Brebbia, C., Telles, J., Wrobel, L.: Boundary Element Techniques: Theory and Practice in Engineering. Springer, Berlin Heidelberg New York (1984)"},{"key":"9625_CR9","volume-title":"Numerical Methods for Laplace Transform Inversion","author":"AM Cohen","year":"2007","unstructured":"Cohen, A.M.: Numerical Methods for Laplace Transform Inversion. Springer, Berlin Heidelberg New York (2007)"},{"issue":"1","key":"9625_CR10","first-page":"231","volume":"BETEQ 2001","author":"A Davies","year":"2002","unstructured":"Davies, A., Crann, D.: Parallel Laplace transform methods for boundary element solutions to diffusion-type problems. J. Boundary Elements BETEQ 2001(1), 231\u2013238 (2002)","journal-title":"J. Boundary Elements"},{"key":"9625_CR11","volume-title":"Integral Transforms and their Applications","author":"B Davies","year":"2005","unstructured":"Davies, B.: Integral Transforms and their Applications, 3rd edn. Springer, Berlin Heidelberg New York (2005)","edition":"3"},{"key":"9625_CR12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0021-9991(79)90025-1","volume":"33","author":"B Davies","year":"1979","unstructured":"Davies, B., Martin, B.: Numerical inversion of the Laplace transform: a survey and comparison of methods. J. Comput. Phys. 33, 1\u201332 (1979). doi: 10.1016\/0021-9991(79)90025-1","journal-title":"J. Comput. Phys."},{"key":"9625_CR13","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1137\/0903022","volume":"3","author":"F Hoog de","year":"1982","unstructured":"de Hoog, F., Knight, J., Stokes, A.: An improved method for numerical inversion of Laplace transforms. SIAM J. Sci. Statist. Comput. 3, 357\u2013366 (1982). doi: 10.1137\/0903022","journal-title":"SIAM J. Sci. Statist. Comput."},{"issue":"3","key":"9625_CR14","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1145\/155743.155788","volume":"19","author":"DG Duffy","year":"1993","unstructured":"Duffy, D.G.: On the numerical inversion of Laplace transforms: comparison of three new methods on characteristic problems from applications. ACM Trans. Math. Softw. 19(3), 333\u2013359 (1993). doi: 10.1145\/155743.155788","journal-title":"ACM Trans. Math. Softw."},{"key":"9625_CR15","doi-asserted-by":"crossref","DOI":"10.1201\/9781420035148","volume-title":"Transform Methods for Solving Partial Differential Equations","author":"DG Duffy","year":"2004","unstructured":"Duffy, D.G.: Transform Methods for Solving Partial Differential Equations. CRC Press, Boca Raton, FL (2004)"},{"issue":"11","key":"9625_CR16","doi-asserted-by":"crossref","first-page":"3713","DOI":"10.1029\/JZ065i011p03713","volume":"65","author":"M Hantush","year":"1960","unstructured":"Hantush, M.: Modification of the theory of leaky aquifers. J. Geophys. Res. 65(11), 3713\u20133725 (1960). doi: 10.1029\/JZ065i011p03713","journal-title":"J. Geophys. Res."},{"key":"9625_CR17","unstructured":"Johansson, F.: mpmath: a Python library for arbitrary-precision floating-point arithmetic (version 0.17). http:\/\/code.google.com\/p\/mpmath\/ (2011). Accessed Dec 2011"},{"issue":"3","key":"9625_CR18","doi-asserted-by":"crossref","first-page":"335","DOI":"10.4310\/CMS.2005.v3.n3.a4","volume":"3","author":"PO Kano","year":"2005","unstructured":"Kano, P.O., Brio, M., Moloney, J.V.: Application of the Weeks method for the numerical inversion of the Laplace transform to the matrix exponential. Communications in Mathematical Sciences 3(3), 335\u2013372 (2005)","journal-title":"Communications in Mathematical Sciences"},{"issue":"2","key":"9625_CR19","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1007\/s10665-008-9251-1","volume":"64","author":"KL Kuhlman","year":"2009","unstructured":"Kuhlman, K.L., Neuman, S.P.: Laplace-transform analytic-element method for transient porous-media flow. J. Eng. Math. 64(2), 113\u2013130 (2009). doi: 10.1007\/s10665-008-9251-1","journal-title":"J. Eng. Math."},{"key":"9625_CR20","volume-title":"An Introduction to Boundary Element Methods","author":"PK Kythe","year":"1995","unstructured":"Kythe, P.K.: An Introduction to Boundary Element Methods. CRC Press, Boca Raton, FL (1995)"},{"key":"9625_CR21","volume-title":"Applied Analysis","author":"C Lanczos","year":"1988","unstructured":"Lanczos, C.: Applied Analysis. Dover, New York (1988)"},{"key":"9625_CR22","volume-title":"The Boundary Integral Equation Method for Porous Media Flow","author":"JA Liggett","year":"1982","unstructured":"Liggett, J.A., Liu, P.L.: The Boundary Integral Equation Method for Porous Media Flow. Unwin, London, UK (1982)"},{"issue":"175","key":"9625_CR23","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1090\/S0025-5718-1986-0842138-1","volume":"47","author":"J Lyness","year":"1986","unstructured":"Lyness, J., Giunta, G.: A modification of the Weeks method for numerical inversion of the Laplace transform. Math. Comput. 47(175), 313\u2013322 (1986). doi: 10.2307\/2008097","journal-title":"Math. Comput."},{"issue":"2","key":"9625_CR24","doi-asserted-by":"crossref","first-page":"990","DOI":"10.1111\/j.1365-246X.2009.04336.x","volume":"179","author":"B Malama","year":"2009","unstructured":"Malama, B., Kuhlman, K., Revil, A.: Theory of transient streaming potentials associated with axial-symmetric flow in unconfined aquifers. Geophys. J. Int. 179(2), 990\u20131003 (2009). doi: 10.1111\/j.1365-246X.2009.04336.x","journal-title":"Geophys. J. Int."},{"issue":"7","key":"9625_CR25","doi-asserted-by":"crossref","first-page":"W07508, 16","DOI":"10.1029\/2009WR008899","volume":"46","author":"PK Mishra","year":"2010","unstructured":"Mishra, P.K., Neuman, S.P.: Improved forward and inverse analyses of saturated-unsaturated flow toward a well in a compressible unconfined aquifer. Water Resour. Res. 46(7), W07508, 16 (2010). doi: 10.1029\/2009WR008899","journal-title":"Water Resour. Res."},{"issue":"1","key":"9625_CR26","doi-asserted-by":"crossref","first-page":"131","DOI":"10.4208\/cicp.2009.v6.p131","volume":"6","author":"E Morales-Casique","year":"2009","unstructured":"Morales-Casique, E., Neuman, S.P.: Laplace-transform finite element solution of nonlocal and localized stochastic moment equations of transport. Commun. Comput. Phys. 6(1), 131\u2013161 (2009)","journal-title":"Commun. Comput. Phys."},{"issue":"3","key":"9625_CR27","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1109\/MCSE.2007.58","volume":"9","author":"TE Oliphant","year":"2007","unstructured":"Oliphant, T.E.: Python for scientific computing. Comput. Sci. Eng. 9(3), 10\u201320 (2007). doi: 10.1109\/MCSE.2007.58","journal-title":"Comput. Sci. Eng."},{"key":"9625_CR28","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1093\/imamat\/10.2.185","volume":"10","author":"R Piessens","year":"1972","unstructured":"Piessens, R.: A new numerical method for the inversion of the Laplace transform. J. Inst. Math. Appl. 10, 185\u2013192 (1972). doi: 10.1093\/imamat\/10.2.185","journal-title":"J. Inst. Math. Appl."},{"key":"9625_CR29","unstructured":"Schapery, R.: Approximate methods of transform inversion for visco-elastic stress analysis. In: Proceedings of the Fourth US National Congress on Applied Mechanics, vol. 2, pp. 1075\u20131085 (1962)"},{"issue":"1","key":"9625_CR30","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1145\/361953.361969","volume":"13","author":"H Stehfest","year":"1970","unstructured":"Stehfest, H.: Algorithm 368: numerical inversion of Laplace transforms. Commun. ACM 13(1), 47\u201349 (1970). doi: 10.1145\/361953.361969","journal-title":"Commun. ACM"},{"issue":"6","key":"9625_CR31","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1111\/j.1745-6584.1969.tb01666.x","volume":"7","author":"Y Sternberg","year":"1969","unstructured":"Sternberg, Y.: Flow to wells in the presence of radial discontinuities. Ground Water 7(6), 17\u201320 (1969). doi: 10.1111\/j.1745-6584.1969.tb01666.x","journal-title":"Ground Water"},{"issue":"2","key":"9625_CR32","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1029\/91WR02560","volume":"28","author":"E Sudicky","year":"1992","unstructured":"Sudicky, E., McLaren, R.: The Laplace transform Galerkin technique for large-scale simulation of mass transport in discretely fractured porous formations. Water Resour. Res. 28(2), 499\u2013514 (1992). doi: 10.1029\/91WR02560","journal-title":"Water Resour. Res."},{"issue":"1","key":"9625_CR33","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1093\/imamat\/23.1.97","volume":"23","author":"A Talbot","year":"1979","unstructured":"Talbot, A.: The accurate numerical inversion of Laplace transforms. IMA J. Appl. Math. 23(1), 97 (1979). doi: 10.1093\/imamat\/23.1.97","journal-title":"IMA J. Appl. Math."},{"issue":"3","key":"9625_CR34","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1145\/321341.321351","volume":"13","author":"W Weeks","year":"1966","unstructured":"Weeks, W.: Numerical inversion of Laplace transforms using Laguerre functions. J. ACM 13(3), 419\u2013429 (1966). doi: 10.1145\/321341.321351","journal-title":"J. ACM"},{"issue":"1","key":"9625_CR35","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1137\/S1064827596312432","volume":"21","author":"J Weideman","year":"1999","unstructured":"Weideman, J.: Algorithms for parameter selection in the Weeks method for inverting the Laplace transform. SIAM J. Sci. Comput. 21(1), 111\u2013128 (1999). doi: 10.1137\/S1064827596312432","journal-title":"SIAM J. Sci. Comput."},{"key":"9625_CR36","volume-title":"The Laplace Transform","author":"D Widder","year":"1941","unstructured":"Widder, D.: The Laplace Transform. Princeton University Press, Princeton, NJ (1941)"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-012-9625-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-012-9625-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-012-9625-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,2]],"date-time":"2019-07-02T06:34:54Z","timestamp":1562049294000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-012-9625-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,8,2]]},"references-count":36,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2013,6]]}},"alternative-id":["9625"],"URL":"https:\/\/doi.org\/10.1007\/s11075-012-9625-3","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,8,2]]}}}