{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T04:44:57Z","timestamp":1775018697155,"version":"3.50.1"},"reference-count":28,"publisher":"Pleiades Publishing Ltd","issue":"5","license":[{"start":{"date-parts":[[2023,10,1]],"date-time":"2023-10-01T00:00:00Z","timestamp":1696118400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,10,1]],"date-time":"2023-10-01T00:00:00Z","timestamp":1696118400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Program Comput Soft"],"published-print":{"date-parts":[[2023,10]]},"DOI":"10.1134\/s0361768823020044","type":"journal-article","created":{"date-parts":[[2023,10,9]],"date-time":"2023-10-09T04:55:24Z","timestamp":1696827324000},"page":"412-422","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["On Implementation of Numerical Methods for Solving Ordinary Differential Equations in Computer Algebra Systems"],"prefix":"10.1134","volume":"49","author":[{"given":"A.","family":"Baddour","sequence":"first","affiliation":[]},{"given":"M. M.","family":"Gambaryan","sequence":"additional","affiliation":[]},{"given":"L.","family":"Gonzalez","sequence":"additional","affiliation":[]},{"given":"M. D.","family":"Malykh","sequence":"additional","affiliation":[]}],"member":"137","published-online":{"date-parts":[[2023,10,9]]},"reference":[{"key":"3755_CR1","unstructured":"Runge, C. and K\u00f6nig, H., Vorlesungen \u00fcber numerisches Rechnen, Springer-Verlag, 2013."},{"key":"3755_CR2","unstructured":"SciPy documentation, 2022. https:\/\/docs.scipy.org."},{"key":"3755_CR3","doi-asserted-by":"publisher","first-page":"175","DOI":"10.2140\/camcos.2014.9.175","volume":"9","author":"D.I. Ketcheson","year":"2014","unstructured":"Ketcheson, D.I. and Waheed, U., A comparison of high order explicit Runge\u2013Kutta, extrapolation, and deferred correction methods in serial and parallel, CAMCoS, 2014, vol. 9, no. 2, pp. 175\u2013200.","journal-title":"CAMCoS"},{"key":"3755_CR4","unstructured":"Gevorkyan, M.N., Concrete implementations of symplectic numerical methods, Vestn. Ross. Univ. Druzhby Nar., Ser. Mat., Inf., \n               Fiz., 2013, no. 3, pp. 77\u201389."},{"key":"3755_CR5","doi-asserted-by":"publisher","DOI":"10.1201\/b14575","volume-title":"Mimetic Discretization Methods","author":"J.E. Castillo","year":"2013","unstructured":"Castillo, J.E. and Miranda, G.F., Mimetic Discretization Methods, Chapman and Hall\/CRC, 2013."},{"key":"3755_CR6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-02663-3","volume-title":"The mimetic finite difference method for elliptic problems","author":"L.B. Da Veiga","year":"2014","unstructured":"Da Veiga, L.B., Lipnikov, K., and Manzini, G., The mimetic finite difference method for elliptic problems, 2014, vol. 11."},{"key":"3755_CR7","volume-title":"Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations","author":"E. Hairer","year":"2000","unstructured":"Hairer, E., Wanner, G., and Lubich, Ch., Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations, New York: Springer, 2000."},{"key":"3755_CR8","doi-asserted-by":"crossref","unstructured":"Ying, Yu, Baddour, A., Gerdt, V.P., et al., On the quadratization of the integrals for the many-body problem, Mathematics, 2021, vol. 9, no. 24.","DOI":"10.3390\/math9243208"},{"key":"3755_CR9","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1134\/S1547477122010022","volume":"19","author":"A. Baddour","year":"2022","unstructured":"Baddour, A. and Malykh, M., On difference schemes for the many-body problem preserving all algebraic integrals, Phys. Part. Nucl. Lett., 2022, vol. 19, pp. 77\u201380.","journal-title":"Phys. Part. Nucl. Lett."},{"key":"3755_CR10","doi-asserted-by":"publisher","first-page":"698","DOI":"10.1007\/s10958-022-05781-4","volume":"261","author":"A. Baddour","year":"2022","unstructured":"Baddour, A., Malykh, M., and Sevastianov, L., On periodic approximate solutions of dynamical systems with quadratic right-hand side, J. Math. Sci., 2022, vol. 261, pp. 698\u2013708.","journal-title":"J. Math. Sci."},{"key":"3755_CR11","unstructured":"Stein, W.A., Sage Mathematics Software (Version 6.7), 2015. http:\/\/ www.sagemath.org."},{"key":"3755_CR12","first-page":"285","volume":"26","author":"M.D. Malykh","year":"2018","unstructured":"Malykh, M.D. and Ying, Yu, Technique for finding algebraic integrals of first-order differential equations, Vestn. Ross. Univ. Druzhby Nar., Ser. Mat., Inf., \n               Fiz., 2018, vol. 26, no. 3, pp. 285\u2013291.","journal-title":"Fiz."},{"key":"3755_CR13","unstructured":"Kalitkin, N.N., Al\u2019shin, A.B., Al\u2019shina, E.A., and Rogov, B.V., Vychisleniya na kvaziravnomernykh setkakh (Computations on Quasi-Uniform Grids), Moscow: Fizmatlit, 2005."},{"key":"3755_CR14","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1134\/S1064562416010129","volume":"93","author":"A.A. Belov","year":"2016","unstructured":"Belov, A.A., Kalitkin, N.N., and Poshivaylo, I.P., Geometrically adaptive grids for stiff Cauchy problems, Dokl. Math., 2016, vol. 93, no. 1, pp. 112\u2013116.","journal-title":"Dokl. Math."},{"key":"3755_CR15","doi-asserted-by":"publisher","first-page":"638","DOI":"10.1134\/S2070048216060065","volume":"8","author":"A.A. Belov","year":"2016","unstructured":"Belov, A.A. and Kalitkin, N.N., Nonlinearity problem in the numerical solution of superstiff Cauchy problems, Math. Models Comput. Simul., 2016, vol. 8, no. 6, pp. 638\u2013650.","journal-title":"Math. Models Comput. Simul."},{"key":"3755_CR16","doi-asserted-by":"publisher","first-page":"230","DOI":"10.1134\/S1064562419020273","volume":"99","author":"A.A. Belov","year":"2019","unstructured":"Belov, A.A., Kalitkin, N.N., Bulatov, P.E., and Zholkovskii, E.K., Explicit methods for integrating stiff Cauchy problems, Dokl. Math., 2019, vol. 99, no. 2, pp.\u00a0230\u2013234.","journal-title":"Dokl. Math."},{"key":"3755_CR17","doi-asserted-by":"publisher","first-page":"271","DOI":"10.22363\/2658-4670-2021-29-3-271-284","volume":"29","author":"A. Baddour","year":"2021","unstructured":"Baddour, A. and Malykh, M.D., Richardson\u2013Kalitkin method in abstract description, Discrete Contin. Models Appl. Comput. Sci., 2021, vol. 29, no. 3, pp. 271\u2013284.","journal-title":"Discrete Contin. Models Appl. Comput. Sci."},{"key":"3755_CR18","doi-asserted-by":"publisher","first-page":"17","DOI":"10.22363\/2658-4670-2020-28-1-17-34","volume":"28","author":"A. Baddour","year":"2020","unstructured":"Baddour, A., Malykh, M.D., Panin, A.A., and Sevastianov, L.A., Numerical determination of the singularity order of a system of differential equations, Discrete Contin. Models Appl. Comput. Sci., 2020, vol. 28, no. 1, pp. 17\u201334.","journal-title":"Discrete Contin. Models Appl. Comput. Sci."},{"key":"3755_CR19","volume-title":"Solving Ordinary Differential Equations I","author":"E. Hairer","year":"2008","unstructured":"Hairer, E., Wanner, G., and Norsett, S.P., Solving Ordinary Differential Equations I, Springer, 2008, 3rd ed."},{"key":"3755_CR20","first-page":"33","volume":"27","author":"Yu Ying","year":"2019","unstructured":"Ying, Yu, The symbolic problems associated with Runge\u2013Kutta methods and their solving in Sage, Discrete Contin. \n               Models Appl. Comput. Sci., 2019, vol. 27, no. 1, pp. 33\u201341.","journal-title":"Models Appl. Comput. Sci."},{"key":"3755_CR21","unstructured":"Khashin, S.I., Numerical solution of Butcher equations, Vestn. Ivanovskogo Gos. Univ., 2000, no. 3, pp.\u00a0155\u2013164."},{"key":"3755_CR22","unstructured":"Khammud, G.M. and Khashin, S.I., Six-dimensional family of 5-order 6-step Runge\u2013Kutta methods, Nauch. Tr. Ivanovskogo Gos. Univ., \n               Mat., 2001, no. 4, pp. 114\u2013122."},{"key":"3755_CR23","unstructured":"Khashin, S.I., Alternative form of Butcher equations, Vestn. Ivanovskogo Gos. Univ., 2007, no. 3, pp. 94\u2013103."},{"key":"3755_CR24","first-page":"555","volume":"17","author":"S.I. Khashin","year":"2009","unstructured":"Khashin, S.I., A symbolic-numeric approach to the solution of the Butcher equations, Can. Appl. Math. Q., 2009, vol. 17, no. 3, pp. 555\u2013569.","journal-title":"Can. Appl. Math. Q."},{"key":"3755_CR25","unstructured":"Khashin, S.I., Three simplifying assumptions for Runge\u2013Kutta Methods, Vestn. Ivanovskogo Gos. Univ., 2012, no. 2, pp. 142\u2013150."},{"key":"3755_CR26","unstructured":"Stone, P., Maple worksheets on the derivation of Runge\u2013Kutta schemes, 2021. http:\/\/www.peterstone.name\/Maplepgs\/RKcoeff.html."},{"key":"3755_CR27","unstructured":"Sikorskii, Yu.S., Elementy teorii ellipticheskikh funktsii s prilozheniyami k mekhanike (Elements of the Theory of Elliptic Functions with Applications to Mechanics), Moscow: ONTI, 1936."},{"key":"3755_CR28","volume-title":"Numerical Mathematical Analysis","author":"J.B. Scarborough","year":"1930","unstructured":"Scarborough, J.B., Numerical Mathematical Analysis, Oxford University Press, 1930."}],"container-title":["Programming and Computer Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0361768823020044.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1134\/S0361768823020044","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0361768823020044.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T02:55:08Z","timestamp":1775012108000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1134\/S0361768823020044"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10]]},"references-count":28,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2023,10]]}},"alternative-id":["3755"],"URL":"https:\/\/doi.org\/10.1134\/s0361768823020044","relation":{},"ISSN":["0361-7688","1608-3261"],"issn-type":[{"value":"0361-7688","type":"print"},{"value":"1608-3261","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,10]]},"assertion":[{"value":"21 June 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 July 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 October 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 October 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare that they have no conflicts of interest.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"CONFLICT OF INTEREST"}}]}}