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Fourteen of these time integrators are recent unconditionally stable algorithms, which are often much more efficient than the mainstream explicit methods. Finally, the adaptive time-step version of some of these algorithms are created and tested versus widespread algorithms, such as the Runge\u2013Kutta\u2013Fehlberg solver.<\/jats:p>","DOI":"10.3390\/a16040184","type":"journal-article","created":{"date-parts":[[2023,3,28]],"date-time":"2023-03-28T07:05:25Z","timestamp":1679987125000},"page":"184","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Analytical and Numerical Results for the Transient Diffusion Equation with Diffusion Coefficient Depending on Both Space and Time"],"prefix":"10.3390","volume":"16","author":[{"given":"Mahmoud","family":"Saleh","sequence":"first","affiliation":[{"name":"Institute of Physics and Electrical Engineering, University of Miskolc, 3515 Miskolc, Hungary"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0439-3070","authenticated-orcid":false,"given":"Endre","family":"Kov\u00e1cs","sequence":"additional","affiliation":[{"name":"Institute of Physics and Electrical Engineering, University of Miskolc, 3515 Miskolc, Hungary"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6206-3910","authenticated-orcid":false,"given":"Imre Ferenc","family":"Barna","sequence":"additional","affiliation":[{"name":"Wigner Research Center for Physics, 1051 Budapest, Hungary"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,28]]},"reference":[{"key":"ref_1","unstructured":"Lienhard, J.H.L., and Lienhard, J.H. 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