López Pouso, ÓscarJumaniyazov, Nizomjon2024-12-202024-12-202021-01-06López Pouso, Ó., & Jumaniyazov, N. (2021). Direct versus iterative methods for forward-backward diffusion equations. Numerical comparisons. SeMA Journal, 78(3), 271-286. https://doi.org/10.1007/S40324-020-00236-92281-7875https://hdl.handle.net/10347/38253This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s40324-020-00236-9By far, the standard implementation of finite difference schemes for forward–backward partial differential equations consists in employing an iterative method. This paper collects a series of numerical results which demonstrate that a direct implementation can reduce the computing time. An effective way of choosing the seed for the iterative method naturally arises.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Forward–backward partial differential equationTwo-way partial differential equationFinite difference methodFokker–Planck equationDirect methodIterative methodjournal article10.1007/s40324-020-00236-9open access