{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T03:37:50Z","timestamp":1777520270909,"version":"3.51.4"},"reference-count":24,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,1,22]],"date-time":"2019-01-22T00:00:00Z","timestamp":1548115200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This paper studies an effective finite difference scheme for solving two-dimensional Heston stochastic volatility option-pricing model problems. A dynamically balanced up-downwind strategy for approximating the cross-derivative is implemented and analyzed. Semi-discretized and spatially nonuniform platforms are utilized. The numerical method comprised is simple and straightforward, with reliable first order overall approximations. The spectral norm is used throughout the investigation, and numerical stability is proven. Simulation experiments are given to illustrate our results.<\/jats:p>","DOI":"10.3390\/a12020030","type":"journal-article","created":{"date-parts":[[2019,1,24]],"date-time":"2019-01-24T03:52:32Z","timestamp":1548301952000},"page":"30","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["An Exploration of a Balanced Up-Downwind Scheme for Solving Heston Volatility Model Equations on Variable Grids"],"prefix":"10.3390","volume":"12","author":[{"given":"Chong","family":"Sun","sequence":"first","affiliation":[{"name":"Department of Mathematics and Center for Astrophysics, Space Physics, and Engineering Research, Baylor University, One Bear Place, Waco, TX 76798-7328, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qin","family":"Sheng","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Center for Astrophysics, Space Physics, and Engineering Research, Baylor University, One Bear Place, Waco, TX 76798-7328, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1137\/S0036144596322507","article-title":"Calculation of weights in finite difference formulas","volume":"40","author":"Fornberg","year":"1998","journal-title":"SIAM Rev."},{"key":"ref_2","first-page":"905","article-title":"An unconditionally monotone numerical scheme for the two-factor uncertain volatility model","volume":"37","author":"Ma","year":"2017","journal-title":"IMA J. 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