{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T11:56:45Z","timestamp":1759838205403,"version":"3.40.5"},"reference-count":29,"publisher":"Walter de Gruyter GmbH","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>A new symbolic algorithmic implementation of the general scheme of the exponentially convergent functional-discrete method is developed and justified for the Sturm\u2013Liouville problem on a finite interval for the Schr\u00f6dinger equation with a polynomial potential and the boundary conditions of Dirichlet type. The algorithm of the general scheme of our method is developed when the potential function is approximated by the piecewise-constant function. Our algorithm is symbolic and operates with the decomposition coefficients of the eigenfunction corrections in some basis.\nThe number of summands in these decompositions depends on the degree of the potential polynomial and on the correction number.\nOur method uses the algebraic operations only and does not need solutions of any boundary value problems and computations of any integrals unlike the previous version.\nA numerical example illustrates the theoretical results.<\/jats:p>","DOI":"10.1515\/cmam-2017-0040","type":"journal-article","created":{"date-parts":[[2017,10,13]],"date-time":"2017-10-13T10:00:49Z","timestamp":1507888849000},"page":"703-715","source":"Crossref","is-referenced-by-count":3,"title":["Symbolic Algorithm of the Functional-Discrete Method for a Sturm\u2013Liouville Problem with a Polynomial Potential"],"prefix":"10.1515","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4883-6574","authenticated-orcid":false,"given":"Volodymyr","family":"Makarov","sequence":"first","affiliation":[{"name":"Department of Numerical Mathematics , Institute of Mathematics of National Academy of Sciences of Ukraine , 3 Tereshchenkivs\u2019ka Str., 01004 Kyiv -4 , Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3497-7077","authenticated-orcid":false,"given":"Nataliia","family":"Romaniuk","sequence":"additional","affiliation":[{"name":"Department of Numerical Mathematics , Institute of Mathematics of National Academy of Sciences of Ukraine , 3 Tereshchenkivs\u2019ka Str., 01004 Kyiv -4 , Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2017,10,13]]},"reference":[{"key":"2023033110390292000_j_cmam-2017-0040_ref_001_w2aab3b7d358b1b6b1ab2ab1Aa","doi-asserted-by":"crossref","unstructured":"E. 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