{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T14:30:05Z","timestamp":1774449005022,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,1,12]],"date-time":"2022-01-12T00:00:00Z","timestamp":1641945600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>An implicit finite difference scheme for the numerical solution of a generalized Black\u2013Scholes equation is presented. The method is based on the nonstandard finite difference technique. The positivity property is discussed and it is shown that the proposed method is consistent, stable and also the order of the scheme respect to the space variable is two. As the Black\u2013Scholes model relies on symmetry of distribution and ignores the skewness of the distribution of the asset, the proposed method will be more appropriate for solving such symmetric models. In order to illustrate the efficiency of the new method, we applied it on some test examples. The obtained results confirm the theoretical behavior regarding the order of convergence. Furthermore, the numerical results are in good agreement with the exact solution and are more accurate than other existing results in the literature.<\/jats:p>","DOI":"10.3390\/sym14010141","type":"journal-article","created":{"date-parts":[[2022,1,12]],"date-time":"2022-01-12T04:15:25Z","timestamp":1641960925000},"page":"141","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Nonstandard Finite Difference Method for a Generalized Black\u2013Scholes Equation"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0130-0449","authenticated-orcid":false,"given":"Mohammad","family":"Mehdizadeh Khalsaraei","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh 83111-55181, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammad Mehdi","family":"Rashidi","sequence":"additional","affiliation":[{"name":"Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China"},{"name":"Faculty of Mechanical and Industrial Engineering, Quchan University of Technology, Quchan 94771-67335, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2699-1490","authenticated-orcid":false,"given":"Ali","family":"Shokri","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh 83111-55181, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2791-6230","authenticated-orcid":false,"given":"Higinio","family":"Ramos","sequence":"additional","affiliation":[{"name":"Scientific Computing Group, Universidad de Salamanca, Plaza de la Merced, 37008 Salamanca, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5012-4990","authenticated-orcid":false,"given":"Pari","family":"Khakzad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh 83111-55181, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1086\/260062","article-title":"The pricing of options and corporate liabilities","volume":"81","author":"Black","year":"1973","journal-title":"J. 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