{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,9,28]],"date-time":"2022-09-28T00:50:31Z","timestamp":1664326231566},"reference-count":10,"publisher":"Association for Computing Machinery (ACM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. ACM"],"published-print":{"date-parts":[[1968,1]]},"abstract":"In this paper the problem of readily determining the inverse Laplace transform numerically by a method which meets the efficiency requirements of automatic digital computation is discussed. Because the result inverse function is given as a Fourier cosine series, the procedure requires only about ten FORTRAN statements. Furthermore, it does not require the use of involved algorithms for the generation of any special functions, but uses only cosines and exponentials.<\/jats:p>\n The basis of the method hinges on the fact that in evaluating the inverse Laplace transform integral there exists a freedom in choosing the contour of integration. Given certain restrictions, the contour may be any vertical line in the right-half plane. Specifying a line, the integral to be evaluated is essentially a Fourier integral. However, the method is concerned with determining the proper line, so that when the integral (along this line) is approximated, the error is as small as desired by virtue of having chosen the particular contour.<\/jats:p>","DOI":"10.1145\/321439.321446","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T11:26:10Z","timestamp":1027769170000},"page":"115-123","source":"Crossref","is-referenced-by-count":364,"title":["Numerical Inversion of Laplace Transforms by Relating Them to the Finite Fourier Cosine Transform"],"prefix":"10.1145","volume":"15","author":[{"given":"H.","family":"Dubner","sequence":"first","affiliation":[{"name":"Computer Applicalions, Inc., New York, New York"}]},{"given":"J.","family":"Abate","sequence":"additional","affiliation":[{"name":"Computer Applicalions, Inc., New York, New York"}]}],"member":"320","reference":[{"key":"e_1_2_1_1_2","doi-asserted-by":"publisher","DOI":"10.1145\/367149.367172"},{"key":"e_1_2_1_2_2","unstructured":"HURWITZ H. AND ZWEXFEL P.F. Numerical quadrature of Fourier transform integrals. Math. Tables and Other Aids to Comput. 10 (1956) 140-149. HURWITZ H. AND ZWEXFEL P.F. Numerical quadrature of Fourier transform integrals. Math. Tables and Other Aids to Comput. 10 (1956) 140-149."},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1145\/321341.321351"},{"key":"e_1_2_1_4_2","first-page":"405","article-title":"A new method of inversion of the Laplace transform","volume":"14","author":"PA LiS","year":"1956","journal-title":"Quart. Appl. Math."},{"key":"e_1_2_1_5_2","volume-title":"American Elsevier","author":"BELLMAN R.","year":"1966"},{"key":"e_1_2_1_6_2","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1090\/S0025-5718-1966-0203976-9","article-title":"The calculation of Fourier integrals","volume":"20","author":"DE BALBINE G.","year":"1966","journal-title":"Math. Comp."},{"key":"e_1_2_1_7_2","unstructured":"CIURCHILL R.V. Fourier Series. McGraw-Hill New York 1941. CIURCHILL R.V. Fourier Series. McGraw-Hill New York 1941."},{"key":"e_1_2_1_8_2","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1090\/S0025-5718-1965-0178586-1","article-title":"An algorithm for the machine calculation of complex Fourier series","volume":"19","author":"COOLE","year":"1965","journal-title":"Math. Comp."},{"key":"e_1_2_1_9_2","first-page":"563","volume-title":"Proc. AFIPS 1966 Fall Joint Comput. Confer.","volume":"29","author":"GENTLEMAN W. M."},{"key":"e_1_2_1_10_2","first-page":"79","article-title":"Application of the fast Fourier transform to computation of Fourier integrals, Fourier series, and convolution integrals","volume":"15","author":"COOLE","year":"1967","journal-title":"IEEE Trans."}],"container-title":["Journal of the ACM"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/321439.321446","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,3]],"date-time":"2021-03-03T00:03:32Z","timestamp":1614729812000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/321439.321446"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1968,1]]},"references-count":10,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1968,1]]}},"alternative-id":["10.1145\/321439.321446"],"URL":"http:\/\/dx.doi.org\/10.1145\/321439.321446","relation":{},"ISSN":["0004-5411","1557-735X"],"issn-type":[{"value":"0004-5411","type":"print"},{"value":"1557-735X","type":"electronic"}],"subject":["Artificial Intelligence","Hardware and Architecture","Information Systems","Control and Systems Engineering","Software"],"published":{"date-parts":[[1968,1]]}}}