{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T07:45:51Z","timestamp":1773819951790,"version":"3.50.1"},"reference-count":47,"publisher":"Walter de Gruyter GmbH","issue":"4","funder":[{"DOI":"10.13039\/501100003443","name":"Ministry of Education and Science of the Russian Federation","doi-asserted-by":"publisher","award":["3.1761.2017\/4.6"],"award-info":[{"award-number":["3.1761.2017\/4.6"]}],"id":[{"id":"10.13039\/501100003443","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002261","name":"Russian Foundation for Basic Research","doi-asserted-by":"publisher","award":["16-01-00197"],"award-info":[{"award-number":["16-01-00197"]}],"id":[{"id":"10.13039\/501100002261","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018,10,1]]},"abstract":"Abstract<\/jats:title>\n It is well known that the equation \n \n \n \n \n \n x<\/m:mi>\n \u2032<\/m:mo>\n <\/m:msup>\n \u2062<\/m:mo>\n \n (<\/m:mo>\n t<\/m:mi>\n )<\/m:mo>\n <\/m:mrow>\n <\/m:mrow>\n =<\/m:mo>\n \n \n A<\/m:mi>\n \u2062<\/m:mo>\n x<\/m:mi>\n \u2062<\/m:mo>\n \n (<\/m:mo>\n t<\/m:mi>\n )<\/m:mo>\n <\/m:mrow>\n <\/m:mrow>\n +<\/m:mo>\n \n f<\/m:mi>\n \u2062<\/m:mo>\n \n (<\/m:mo>\n t<\/m:mi>\n )<\/m:mo>\n <\/m:mrow>\n <\/m:mrow>\n <\/m:mrow>\n <\/m:mrow>\n <\/m:math>\n \n {x^{\\prime}(t)=Ax(t)+f(t)}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>, where A<\/jats:italic> is a square matrix, has a unique bounded solution x<\/jats:italic> for any bounded continuous free term f<\/jats:italic>, provided the coefficient A<\/jats:italic> has no eigenvalues on the imaginary axis. This solution can be represented in the form<\/jats:p>\n \n \n \n \n \n \n \n x<\/m:mi>\n \u2062<\/m:mo>\n \n (<\/m:mo>\n t<\/m:mi>\n )<\/m:mo>\n <\/m:mrow>\n <\/m:mrow>\n =<\/m:mo>\n \n \n \u222b<\/m:mo>\n \n -<\/m:mo>\n \u221e<\/m:mi>\n <\/m:mrow>\n \u221e<\/m:mi>\n <\/m:msubsup>\n \n \ud835\udca2<\/m:mi>\n \u2062<\/m:mo>\n \n (<\/m:mo>\n \n t<\/m:mi>\n -<\/m:mo>\n s<\/m:mi>\n <\/m:mrow>\n )<\/m:mo>\n <\/m:mrow>\n \u2062<\/m:mo>\n f<\/m:mi>\n \u2062<\/m:mo>\n \n (<\/m:mo>\n s<\/m:mi>\n )<\/m:mo>\n <\/m:mrow>\n \u2062<\/m:mo>\n \n \ud835\udc51<\/m:mo>\n s<\/m:mi>\n <\/m:mrow>\n <\/m:mrow>\n <\/m:mrow>\n <\/m:mrow>\n .<\/m:mo>\n <\/m:mrow>\n <\/m:math>\n \n x(t)=\\int_{-\\infty}^{\\infty}\\mathcal{G}(t-s)f(s)\\,ds.<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:disp-formula>\n <\/jats:p>\n The kernel \n \n \n \ud835\udca2<\/m:mi>\n <\/m:math>\n \n {\\mathcal{G}}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula> is called Green\u2019s function. In this paper, for approximate calculation of \n \n \n \ud835\udca2<\/m:mi>\n <\/m:math>\n \n {\\mathcal{G}}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>, the Newton interpolating polynomial of a special function \n \n \n \n g<\/m:mi>\n t<\/m:mi>\n <\/m:msub>\n <\/m:math>\n \n {g_{t}}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula> is used. An estimate of the sensitivity of the problem is given. The results of numerical experiments are presented.<\/jats:p>","DOI":"10.1515\/cmam-2017-0042","type":"journal-article","created":{"date-parts":[[2017,10,12]],"date-time":"2017-10-12T10:00:45Z","timestamp":1507802445000},"page":"673-685","source":"Crossref","is-referenced-by-count":6,"title":["Computation of Green\u2019s Function of the Bounded Solutions Problem"],"prefix":"10.1515","volume":"18","author":[{"given":"Vitalii G.","family":"Kurbatov","sequence":"first","affiliation":[{"name":"Department of Mathematical Physics , Voronezh State University , 1 Universitetskaya Square , Voronezh 394018 , Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Irina V.","family":"Kurbatova","sequence":"additional","affiliation":[{"name":"Department of Software Development and Information Systems Administration , Voronezh State University , 1 Universitetskaya Square , Voronezh 394018 , Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2017,10,12]]},"reference":[{"key":"2023033110390287024_j_cmam-2017-0042_ref_001_w2aab3b7d808b1b6b1ab2ab1Aa","doi-asserted-by":"crossref","unstructured":"E. 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