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It is assumed that this approach is used to handle non-linear systems of ordinary differential equations (ODEs) which arise often in the mathematical description of scientific and engineering models either directly or after the discretization of the spatial derivatives of partial differential equations (PDEs). The major topic is the analysis of<jats:italic>eight<\/jats:italic>advanced implementations of the Richardson Extrapolation. Two important properties are analyzed: (a) the possibility to achieve<jats:italic>more accurate results<\/jats:italic>and (b) the possibility to improve<jats:italic>the stability properties<\/jats:italic>of eight advanced versions of the Richardson Extrapolation. A two-parameter family of test-examples was constructed and used to check both the accuracy and the absolute stability of the different versions of the Richardson Extrapolation when these versions are applied together with several Explicit Runge\u2013Kutta Methods (ERKMs).<\/jats:p>","DOI":"10.1515\/cmam-2019-0016","type":"journal-article","created":{"date-parts":[[2019,7,19]],"date-time":"2019-07-19T09:03:22Z","timestamp":1563527002000},"page":"739-762","source":"Crossref","is-referenced-by-count":11,"title":["Explicit Runge\u2013Kutta Methods Combined with Advanced Versions of the Richardson Extrapolation"],"prefix":"10.1515","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4904-7486","authenticated-orcid":false,"given":"Zahari","family":"Zlatev","sequence":"first","affiliation":[{"name":"Department of Environmental Science , Aarhus University , Roskilde , Denmark"}]},{"given":"Ivan","family":"Dimov","sequence":"additional","affiliation":[{"name":"Institute of Information and Communication Technologies , Bulgarian Academy of Sciences , Sofia , Bulgaria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4615-7615","authenticated-orcid":false,"given":"Istv\u00e1n","family":"Farag\u00f3","sequence":"additional","affiliation":[{"name":"Institute of Mathematics , Budapest University of Technology and Economics , Egry J. u. 1., 1111 , Budapest , Hungary"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5277-2887","authenticated-orcid":false,"given":"Krassimir","family":"Georgiev","sequence":"additional","affiliation":[{"name":"Institute of Information and Communication Technologies , Bulgarian Academy of Sciences , Sofia , Bulgaria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4125-4520","authenticated-orcid":false,"given":"\u00c1gnes","family":"Havasi","sequence":"additional","affiliation":[{"name":"MTA-ELTE Numerical Analysis and Large Networks Research Group ; and Department of Applied Analysis and Computational Mathematics, E\u00f6tv\u00f6s Lor\u00e1nd University , Budapest , Hungary"}]}],"member":"374","published-online":{"date-parts":[[2019,7,16]]},"reference":[{"key":"2023033110450848117_j_cmam-2019-0016_ref_001","doi-asserted-by":"crossref","unstructured":"S. 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