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The error of the numerical solution with respect to the exact solution is due to this approximation as well as to a possible perturbation in the initial value. For an unperturbed initial value, we have found: (1) unlike the absolute error, the relative error always grows linearly in time; (2) in the long-time, the contributions to the relative error relevant to non-rightmost eigenvalues of <jats:italic>A<\/jats:italic> disappear.<\/jats:p>","DOI":"10.1515\/jnma-2020-0019","type":"journal-article","created":{"date-parts":[[2020,11,30]],"date-time":"2020-11-30T21:08:24Z","timestamp":1606770504000},"page":"119-158","source":"Crossref","is-referenced-by-count":2,"title":["Relative error analysis of matrix exponential approximations for numerical integration"],"prefix":"10.1515","volume":"29","author":[{"given":"Stefano","family":"Maset","sequence":"first","affiliation":[{"name":"Universit\u00e0 di Trieste, Dipartimento di Matematica e Geoscienze, Via Valerio 12\/A , 34127 , Trieste , Italy"}]}],"member":"374","published-online":{"date-parts":[[2021,7,3]]},"reference":[{"key":"2025050812064118807_j_jnma-2020-0019_ref_001_w2aab3b7b3b1b6b1ab2b1b1Aa","doi-asserted-by":"crossref","unstructured":"F. 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