{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T14:15:46Z","timestamp":1775484946951,"version":"3.50.1"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,12,21]],"date-time":"2023-12-21T00:00:00Z","timestamp":1703116800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,12,21]],"date-time":"2023-12-21T00:00:00Z","timestamp":1703116800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"Study on the percolation characteristics of Shale Gas Reservoirs","award":["2015JY0245"],"award-info":[{"award-number":["2015JY0245"]}]},{"name":"Xihua University graduate course Ideological and political demonstration course","award":["YJSKC202204"],"award-info":[{"award-number":["YJSKC202204"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2024,2]]},"DOI":"10.1007\/s12190-023-01958-5","type":"journal-article","created":{"date-parts":[[2023,12,21]],"date-time":"2023-12-21T06:01:38Z","timestamp":1703138498000},"page":"175-195","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Application of elastic transformation method and similarity construction method in solving ordinary differential equations"],"prefix":"10.1007","volume":"70","author":[{"given":"Tingrong","family":"Jiang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-3747-3740","authenticated-orcid":false,"given":"Pengshe","family":"Zheng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lin","family":"Xu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lihui","family":"Leng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,12,21]]},"reference":[{"key":"1958_CR1","doi-asserted-by":"publisher","first-page":"565","DOI":"10.1088\/0253-6102\/42\/4\/565","volume":"42","author":"SF Shen","year":"2004","unstructured":"Shen, S.F., Pan, Z.L., Zhang, J.: Variable separation approach to solve nonlinear systems. Commun. Theor. Phys. 42, 565 (2004)","journal-title":"Commun. Theor. Phys."},{"key":"1958_CR2","doi-asserted-by":"publisher","first-page":"431","DOI":"10.3969\/j.issn.1001-4748.2020.04.006","volume":"35","author":"GJ Ren","year":"2020","unstructured":"Ren, G.J.: The application of variation of constants in differential and difference equations. J. Shandong Normal Univ. (Nat. Sci.) 35, 431\u2013435 (2020). https:\/\/doi.org\/10.3969\/j.issn.1001-4748.2020.04.006. (Chinese)","journal-title":"J. Shandong Normal Univ. (Nat. Sci.)"},{"key":"1958_CR3","unstructured":"Qi, Y.H., Pugua, C.R.: Application of integrating factor method in solving ordinary differential equations. Math. Learn. Res., 5\u20136 (2017). (Chinese)"},{"key":"1958_CR4","doi-asserted-by":"publisher","first-page":"241","DOI":"10.3969\/j.issn.1673-8462.2000.04.001","volume":"6","author":"SK Meng","year":"2000","unstructured":"Meng, S.K.: Riccati differential equation and its power series solution. J. Guangxi Univ. Nat. (Nat. Sci. Ed.) 6, 241\u2013244 (2000). https:\/\/doi.org\/10.3969\/j.issn.1673-8462.2000.04.001. (Chinese)","journal-title":"J. Guangxi Univ. Nat. (Nat. Sci. Ed.)"},{"key":"1958_CR5","volume-title":"Ordinary Differential Euations and Boundary Value Problems","author":"GX Wang","year":"2008","unstructured":"Wang, G.X., Zhou, Z.M., Zhu, M.S., Wang, S.S.: Ordinary Differential Euations and Boundary Value Problems. Science Press, Beijing (2008). (Chinese)"},{"issue":"8","key":"1958_CR6","doi-asserted-by":"publisher","first-page":"6008","DOI":"10.1016\/j.apm.2012.12.007","volume":"37","author":"H Fatoorehchi","year":"2013","unstructured":"Fatoorehchi, H., Abolghasemi, H.: Improving the differential transform method: a novel technique to obtain the differential transforms of nonlinearities by the Adomian polynomials. Appl. Math. Modell. 37(8), 6008\u20136017 (2013). https:\/\/doi.org\/10.1016\/j.apm.2012.12.007","journal-title":"Appl. Math. Modell."},{"issue":"2","key":"1958_CR7","doi-asserted-by":"publisher","first-page":"729","DOI":"10.1016\/j.amc.2005.09.105","volume":"177","author":"SA El-Wakil","year":"2006","unstructured":"El-Wakil, S.A., Abdou, M.A., Elhanbal, A.: Adomian decomposition method for solving the diffusion\u2013convection\u2013reaction equations. Appl. Math. Comput. 177(2), 729\u2013736 (2006). https:\/\/doi.org\/10.1016\/j.amc.2005.09.105","journal-title":"Appl. Math. Comput."},{"issue":"8","key":"1958_CR8","doi-asserted-by":"publisher","first-page":"1299","DOI":"10.1080\/00207160.2015.1045421","volume":"93","author":"H Fatoorehchi","year":"2015","unstructured":"Fatoorehchi, H., Abolghasemi, H.: Series solution of nonlinear differential equations by a novel extension of the Laplace transform method. Int. J. Comput. Math. 93(8), 1299\u20131319 (2015). https:\/\/doi.org\/10.1080\/00207160.2015.1045421","journal-title":"Int. J. Comput. Math."},{"issue":"3","key":"1958_CR9","doi-asserted-by":"publisher","first-page":"1854","DOI":"10.1016\/j.nonrwa.2008.02.026","volume":"10","author":"RY Molliq","year":"2009","unstructured":"Molliq, R.Y., Noorani, M.S.M., Hashim, I.: Variational iteration method for fractional heat- and wave-like equations. Nonlinear Anal.: Real World Appl. 10(3), 1854\u20131869 (2009). https:\/\/doi.org\/10.1016\/j.nonrwa.2008.02.026","journal-title":"Nonlinear Anal.: Real World Appl."},{"issue":"10","key":"1958_CR10","doi-asserted-by":"publisher","first-page":"3932","DOI":"10.1108\/EC-10-2020-0604","volume":"38","author":"AK Verma","year":"2021","unstructured":"Verma, A.K., Kumar, N., Singh, M., et al.: A note on variation iteration method with an application on Lane-Emden equations. Eng. Comput. 38(10), 3932\u20133943 (2021)","journal-title":"Eng. Comput."},{"issue":"4","key":"1958_CR11","doi-asserted-by":"publisher","first-page":"699","DOI":"10.1016\/S0020-7462(98)00048-1","volume":"34","author":"JH He","year":"1999","unstructured":"He, J.H.: Variational iteration method-a kind of non-linear analytical technique: some examples. Int. J. Non-linear Mech. 34(4), 699\u2013708 (1999)","journal-title":"Int. J. Non-linear Mech."},{"issue":"38","key":"1958_CR12","doi-asserted-by":"publisher","first-page":"5944","DOI":"10.1016\/j.physleta.2008.07.060","volume":"372","author":"T \u00d6zi\u015f","year":"2008","unstructured":"\u00d6zi\u015f, T., A\u011f\u0131rseven, D.: He\u2019s homotopy perturbation method for solving heat-like and wave-like equations with variable coefficients. Phys. Lett. A 372(38), 5944\u20135950 (2008). https:\/\/doi.org\/10.1016\/j.physleta.2008.07.060","journal-title":"Phys. Lett. A"},{"key":"1958_CR13","doi-asserted-by":"publisher","DOI":"10.1007\/s12591-017-0385-3","author":"M Chandru","year":"2017","unstructured":"Chandru, M., Prabha, T., Das, P., Shanthi, V.: A numerical method for solving boundary and interior layers dominated parabolic problems with discontinuous convection coefficient and source terms. Differ. Equs. Dyn. Syst. (2017). https:\/\/doi.org\/10.1007\/s12591-017-0385-3","journal-title":"Differ. Equs. Dyn. Syst."},{"key":"1958_CR14","doi-asserted-by":"publisher","unstructured":"Sci global. Multidomain Legendre-Galerkin Least-Squares Method for Linear Differential Equations with Variable Coefficients. Numer. Math.: Theory Methods Appl. (2020). https:\/\/doi.org\/10.4208\/nmtma.oa-2019-0015","DOI":"10.4208\/nmtma.oa-2019-0015"},{"key":"1958_CR15","doi-asserted-by":"publisher","DOI":"10.1007\/BF01076006","author":"LR Volevich","year":"1968","unstructured":"Volevich, L.R., Gindikin, S.G.: Pseudo-differential operators and Cauchy problem for differential equations with variable coefficients. Funct. Anal. Appl. (1968). https:\/\/doi.org\/10.1007\/BF01076006","journal-title":"Funct. Anal. Appl."},{"key":"1958_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/S40314-022-02111-X","author":"M Akram","year":"2022","unstructured":"Akram, M., Muhammad, G., Allahviranloo, T., Pedrycz, W.: Solution of initial-value problem for linear third-order fuzzy differential equations. Comput. Appl. Math. (2022). https:\/\/doi.org\/10.1007\/S40314-022-02111-X","journal-title":"Comput. Appl. Math."},{"key":"1958_CR17","doi-asserted-by":"publisher","DOI":"10.1007\/S11565-021-00372-8","author":"L Adel","year":"2021","unstructured":"Adel, L., Abdelouaheb, A., Ahcene, D.: Initial value problems of nonlinear fractional differential equations with two orders. Annali dell\u2019universita\u2019 di ferrara (2021). https:\/\/doi.org\/10.1007\/S11565-021-00372-8","journal-title":"Annali dell\u2019universita\u2019 di ferrara"},{"key":"1958_CR18","doi-asserted-by":"publisher","DOI":"10.12691\/tjant-3-6-3;10.12691\/tjant-3-6-3","author":"G Tingting","year":"2015","unstructured":"Tingting, G.: The solutions of initial value problems for second-order Integro-differential equations with delayed arguments in Banach spaces. Turk. J. Anal. Number Theory (2015). https:\/\/doi.org\/10.12691\/tjant-3-6-3;10.12691\/tjant-3-6-3","journal-title":"Turk. J. Anal. Number Theory"},{"key":"1958_CR19","first-page":"16","volume":"06","author":"CZ Huang","year":"1991","unstructured":"Huang, C.Z.: Solution of multidimensional Terzagy consolidation differential equation. Port Eng. 06, 16\u201323 (1991)","journal-title":"Port Eng."},{"issue":"1115\/1","key":"1958_CR20","first-page":"4043676","volume":"10","author":"H Fatoorehchi","year":"2019","unstructured":"Fatoorehchi, H., Alidadi, M., Rach, R., Shojaeian, A.: Theoretical and experimental investigation of thermal dynamics of Steinhart-Hart NTC thermistors. J. Heat Transf. 10(1115\/1), 4043676 (2019)","journal-title":"J. Heat Transf."},{"key":"1958_CR21","doi-asserted-by":"publisher","first-page":"44","DOI":"10.16722\/j.issn.1674-537X.2017.09.015","volume":"09","author":"Wang Weizhu","year":"2017","unstructured":"Weizhu, Wang: Application examples based on differential equation in geometry and economics. Stat. Manag. 09, 44\u201345 (2017). https:\/\/doi.org\/10.16722\/j.issn.1674-537X.2017.09.015","journal-title":"Stat. Manag."},{"key":"1958_CR22","unstructured":"Zhang, J.P.: The general concept of elasticity coefficient. Tech. Econ. (1995) (Chinese)"},{"key":"1958_CR23","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1093\/bioinformatics\/13.2.123","volume":"13","author":"JH Woods","year":"1997","unstructured":"Woods, J.H., Sauro, H.M.: Elasticities in metabolic control analysis: algebraic derivation of simplified expressions. Bioinformatics 13, 123\u2013130 (1997). https:\/\/doi.org\/10.1093\/bioinformatics\/13.2.123","journal-title":"Bioinformatics"},{"key":"1958_CR24","doi-asserted-by":"publisher","DOI":"10.1016\/J.FOOSTR.2020.100171","author":"Z Wang","year":"2020","unstructured":"Wang, Z., Tian, B., Karleen, S., van der Goot, A.J., Chen, J.: Importance of elasticity on calcium caseinate fiber formation. Food Struct. (Prepublish) (2020). https:\/\/doi.org\/10.1016\/J.FOOSTR.2020.100171","journal-title":"Food Struct. (Prepublish)"},{"key":"1958_CR25","doi-asserted-by":"publisher","first-page":"189","DOI":"10.6052\/1000-0992-21-015","volume":"51","author":"Y Chen","year":"2021","unstructured":"Chen, Y., Zhang, Q., Zhang, Y.F., Xia, B.Z., Liu, X.N., Zhou, X.M., et al.: Research progress ofelastic topological materials. Adv. Mech. 51, 189\u2013256 (2021). https:\/\/doi.org\/10.6052\/1000-0992-21-015","journal-title":"Adv. Mech."},{"key":"1958_CR26","doi-asserted-by":"publisher","first-page":"234301","DOI":"10.7498\/aps.69.20200764","volume":"69","author":"TR Zhang","year":"2020","unstructured":"Zhang, T.R., Mo, R.Y., Hu, J., Chen, S., Wang, C.H., Guo, J.Z.: Interaction between bubble andparticle in spherical liquid cavity surround by an elastic medium. Acta Phys. Sin. 69, 234301 (2020). https:\/\/doi.org\/10.7498\/aps.69.20200764","journal-title":"Acta Phys. Sin."},{"key":"1958_CR27","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1016\/j.econlet.2018.08.040","volume":"172","author":"MA Gomez","year":"2018","unstructured":"Gomez, M.A.: Factor substitution and convergence speed in the neoclassical model with elastic labor supply. Econ. Lett. 172, 89\u201392 (2018). https:\/\/doi.org\/10.1016\/j.econlet.2018.08.040","journal-title":"Econ. Lett."},{"key":"1958_CR28","doi-asserted-by":"publisher","first-page":"280","DOI":"10.1016\/j.petrol.2018.12.042","volume":"175","author":"S Li","year":"2019","unstructured":"Li, S., Zhao, C., Zheng, P., Gui, Q.: Analysis of oil and gas flow characteristics in the reservoir with the elastic outer boundary. J. Petrol. Sci. Eng. 175, 280\u2013285 (2019). https:\/\/doi.org\/10.1016\/j.petrol.2018.12.042","journal-title":"J. Petrol. Sci. Eng."},{"key":"1958_CR29","doi-asserted-by":"publisher","first-page":"1307","DOI":"10.3934\/math.2022077","volume":"7","author":"PS Zheng","year":"2021","unstructured":"Zheng, P.S., Luo, J., Li, S.C., Dong, X.X.: Elastic transformation method for solving ordinary differential equations with variable coefficients. AIMS Math. 7, 1307\u20131320 (2021). https:\/\/doi.org\/10.3934\/math.2022077","journal-title":"AIMS Math."},{"key":"1958_CR30","doi-asserted-by":"publisher","DOI":"10.1007\/S12190-022-01791-2","author":"P Zheng","year":"2022","unstructured":"Zheng, P., Tang, J., Leng, L., Li, S.: Solving nonlinear ordinary differential equations with variable coefficients by elastic transformation method. J. Appl. Math. Comput. (2022). https:\/\/doi.org\/10.1007\/S12190-022-01791-2","journal-title":"J. Appl. Math. Comput."},{"key":"1958_CR31","first-page":"32","volume":"5","author":"S Li","year":"2002","unstructured":"Li, S., Liu, P., Zhao, L.: Analysis of bottomhole pressure under different boundary conditions in composite reservoir. J. Southwest Petrol. Inst. 5, 32\u201333 (2002)","journal-title":"J. Southwest Petrol. Inst."},{"key":"1958_CR32","doi-asserted-by":"publisher","DOI":"10.1007\/s40314-019-0847-z","author":"X Dong","year":"2019","unstructured":"Dong, X., Liu, Z., Li, S.: Similar constructing method for solving nonlinear spherical seepage model with quadratic pressure gradient of three-region composite fractal reservoir. Comput. Appl. Math. (2019). https:\/\/doi.org\/10.1007\/s40314-019-0847-z","journal-title":"Comput. Appl. Math."},{"key":"1958_CR33","first-page":"69","volume":"2","author":"W Xia","year":"2015","unstructured":"Xia, W., Li, S., Gui, D.: Similarity construction method for a class of boundary value problems of complex Tschebycheff equations. J. Shaanxi Univ. Technol. (Nat. Sci. Ed.) 2, 69\u201372 (2015)","journal-title":"J. Shaanxi Univ. Technol. (Nat. Sci. Ed.)"}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-023-01958-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-023-01958-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-023-01958-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,9]],"date-time":"2024-02-09T15:42:37Z","timestamp":1707493357000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-023-01958-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,21]]},"references-count":33,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,2]]}},"alternative-id":["1958"],"URL":"https:\/\/doi.org\/10.1007\/s12190-023-01958-5","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"value":"1598-5865","type":"print"},{"value":"1865-2085","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12,21]]},"assertion":[{"value":"1 August 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 November 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 November 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 December 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"No potential conflict of interest was reported by the authors","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}