{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T13:21:51Z","timestamp":1778505711976,"version":"3.51.4"},"reference-count":23,"publisher":"American Mathematical Society (AMS)","issue":"323","license":[{"start":{"date-parts":[[2021,1,6]],"date-time":"2021-01-06T00:00:00Z","timestamp":1609891200000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100003329","name":"Ministerio de Econom\u00c3\u00ada y Competitividad","doi-asserted-by":"publisher","award":["MTM2016-75465"],"award-info":[{"award-number":["MTM2016-75465"]}],"id":[{"id":"10.13039\/501100003329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100009112","name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","doi-asserted-by":"publisher","award":["MTM2016-75465"],"award-info":[{"award-number":["MTM2016-75465"]}],"id":[{"id":"10.13039\/100009112","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    In this paper a novel contour integral method is proposed for linear convection-diffusion equations. The method is based on the inversion of the Laplace transform and makes use of a contour given by an elliptic arc joined symmetrically to two half-lines. The trapezoidal rule is the chosen integration method for the numerical inversion of the Laplace transform, due to its well-known fast convergence properties when applied to analytic functions. Error estimates are provided as well as careful indications about the choice of several involved parameters. The method selects the elliptic arc in the integration contour by an algorithmic strategy based on the computation of pseudospectral level sets of the discretized differential operator. In this sense the method is general and can be applied to any linear convection-diffusion equation without knowing any a priori information about its pseudospectral geometry. Numerical experiments performed on the Black\u2013Scholes (\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"1 upper D\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mi>D<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">1D<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    ) and Heston (\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"2 upper D\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mn>2<\/mml:mn>\n                            <mml:mi>D<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">2D<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    ) equations show that the method is competitive with other contour integral methods available in the literature.\n                  <\/p>","DOI":"10.1090\/mcom\/3497","type":"journal-article","created":{"date-parts":[[2019,10,30]],"date-time":"2019-10-30T14:54:29Z","timestamp":1572447269000},"page":"1161-1191","source":"Crossref","is-referenced-by-count":8,"title":["Numerical inverse Laplace transform for convection-diffusion equations"],"prefix":"10.1090","volume":"89","author":[{"given":"Nicola","family":"Guglielmi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mar\u00eda","family":"L\u00f3pez-Fern\u00e1ndez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Giancarlo","family":"Nino","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2020,1,6]]},"reference":[{"issue":"2","key":"1","doi-asserted-by":"publisher","first-page":"621","DOI":"10.1137\/16M1070657","article-title":"Fast and oblivious algorithms for dissipative and two-dimensional wave equations","volume":"55","author":"Banjai, L.","year":"2017","journal-title":"SIAM J. 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Hull, Options, Futures and Other Derivatives, 6th ed., Prentice Hall, New Jersey, 2006."},{"issue":"2","key":"7","first-page":"303","article-title":"ADI finite difference schemes for option pricing in the Heston model with correlation","volume":"7","author":"In \u2019t Hout, K. J.","year":"2010","journal-title":"Int. J. Numer. Anal. Model.","ISSN":"https:\/\/id.crossref.org\/issn\/1705-5105","issn-type":"print"},{"key":"8","doi-asserted-by":"crossref","unstructured":"K. J. in \u2019t Hout, ADI Schemes in the Numerical Solution of the Heston PDE, Numerical Analysis and Applied Mathematics, eds. T. E. Simos et.al., AIP Conf. Proc: 936, 2007.","DOI":"10.1063\/1.2790085"},{"issue":"1","key":"9","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/j.apnum.2005.11.011","article-title":"Stability of ADI schemes applied to convection-diffusion equations with mixed derivative terms","volume":"57","author":"in \u2019t Hout, K. J.","year":"2007","journal-title":"Appl. Numer. 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