{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:42:01Z","timestamp":1740123721000,"version":"3.37.3"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2020,10,7]],"date-time":"2020-10-07T00:00:00Z","timestamp":1602028800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,10,7]],"date-time":"2020-10-07T00:00:00Z","timestamp":1602028800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"name":"Institute of Information Technology, VAST","award":["CS 20.01"]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2021,8]]},"DOI":"10.1007\/s11075-020-01016-2","type":"journal-article","created":{"date-parts":[[2020,10,7]],"date-time":"2020-10-07T18:02:51Z","timestamp":1602093771000},"page":"1479-1499","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Simple numerical methods of second- and third-order convergence for solving a fully third-order nonlinear boundary value problem"],"prefix":"10.1007","volume":"87","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6386-7347","authenticated-orcid":false,"given":"Quang A","family":"Dang","sequence":"first","affiliation":[]},{"given":"Quang Long","family":"Dang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,10,7]]},"reference":[{"key":"1016_CR1","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.amc.2015.08.129","volume":"271","author":"M Abushammala","year":"2015","unstructured":"Abushammala, M., Khuri, S.A., Sayfy, A.: A novel fixed point iteration method for the solution of third order boundary value problems. Appl. Math. Comput. 271, 131\u2013141 (2015)","journal-title":"Appl. Math. Comput."},{"key":"1016_CR2","doi-asserted-by":"publisher","DOI":"10.1142\/0266","volume-title":"Boundary Value Problems for Higher Order Differential Equations","author":"RP Agarwal","year":"1986","unstructured":"Agarwal, R.P.: Boundary Value Problems for Higher Order Differential Equations. World Scientific, Singapore (1986)"},{"issue":"1","key":"1016_CR3","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1080\/00207160108805100","volume":"78","author":"EA Al-Said","year":"2001","unstructured":"Al-Said, E.A.: Numerical solutions for system of third-order boundary value problems. Int. J. Comput. Math. 78(1), 111\u2013121 (2001)","journal-title":"Int. J. Comput. Math."},{"key":"1016_CR4","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/S0096-3003(02)00294-1","volume":"142","author":"EA Al-Said","year":"2003","unstructured":"Al-Said, E.A., Noor, M.A.: Cubic splines method for a system of third boundary value problems. Appl. Math. Comput. 142, 195\u2013204 (2003)","journal-title":"Appl. Math. Comput."},{"key":"1016_CR5","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1016\/j.amc.2007.01.031","volume":"190","author":"EA Al-Said","year":"2007","unstructured":"Al-Said, E.A., Noor, M.A.: Numerical solutions of third-order system of boundary value problems. Appl. Math. Comput. 190, 332\u2013338 (2007)","journal-title":"Appl. Math. Comput."},{"issue":"25","key":"1016_CR6","first-page":"1","volume":"2008","author":"Z Bai","year":"2008","unstructured":"Bai, Z.: Existence of solutions for some third-order boundary-value problems. Electron. J. Differential Equations 2008(25), 1\u20136 (2008)","journal-title":"Electron. J. Differential Equations"},{"key":"1016_CR7","doi-asserted-by":"publisher","first-page":"568","DOI":"10.1006\/jmaa.1995.1375","volume":"195","author":"A Cabada","year":"1995","unstructured":"Cabada, A.: The method of lower and upper solutions for third-order periodic boundary value problems. J. Math. Anal. Appl. 195, 568\u2013589 (1995)","journal-title":"J. Math. Anal. Appl."},{"key":"1016_CR8","doi-asserted-by":"publisher","first-page":"373","DOI":"10.1080\/00207169908804816","volume":"71","author":"HN Calagar","year":"1999","unstructured":"Calagar, H.N., Cagalar, S.H., Twizell, E.H.: The numerical solution of third order boundary value problems with fourth degree B-Spline. Int. J. Comput. Math. 71, 373\u2013381 (1999)","journal-title":"Int. J. Comput. Math."},{"key":"1016_CR9","doi-asserted-by":"crossref","unstructured":"Chaurasia, A., Srivastava, P.C., Gupta, Y.: Exponential Spline Approximation for the Solution of Third-Order Boundary Value Problems. In: Balas V., Sharma N., Chakrabarti A. (eds.) Data Management, Analytics and Innovation. Adv. Intell. Syst. Comput. 808 (2019)","DOI":"10.1007\/978-981-13-1402-5_26"},{"issue":"9","key":"1016_CR10","first-page":"637","volume":"2","author":"TS El-Danaf","year":"2008","unstructured":"El-Danaf, T.S.: Quartic nonpolynomial spline solutions for third order Two-Point boundary value problem. Inter. J. Math. Comput. Sci. 2(9), 637\u2013640 (2008)","journal-title":"Inter. J. Math. Comput. Sci."},{"key":"1016_CR11","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1016\/j.nonrwa.2017.01.001","volume":"36","author":"QA Dang","year":"2017","unstructured":"Dang, Q.A., Ngo, T.K.Q.: Existence results and iterative method for solving the cantilever beam equation with fully nonlinear term. Nonlinear Anal. Real World Appl. 36, 56\u201368 (2017)","journal-title":"Real World Appl."},{"key":"1016_CR12","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1007\/s11075-017-0264-6","volume":"76","author":"QA Dang","year":"2017","unstructured":"Dang, Q.A., Dang, Q.L., Ngo, T.K.Q.: A novel efficient method for nonlinear boundary value problems. Numer. Algorithms 76, 427\u2013439 (2017)","journal-title":"Numer. Algorithms"},{"issue":"4","key":"1016_CR13","doi-asserted-by":"publisher","first-page":"209","DOI":"10.5269\/bspm.v36i4.33584","volume":"36","author":"QA Dang","year":"2018","unstructured":"Dang, Q.A., Ngo, T.K.Q.: New fixed point approach for a fully nonlinear fourth order boundary value problem. Bol. Soc. Paran. Mat. 36(4), 209\u2013223 (2018)","journal-title":"Bol. Soc. Paran. Mat."},{"issue":"2","key":"1016_CR14","doi-asserted-by":"publisher","first-page":"323","DOI":"10.4208\/eajam.231017.250118a","volume":"8","author":"QA Dang","year":"2018","unstructured":"Dang, Q.A., Nguyen, T.H.: The unique solvability and approximation of BVP for a nonlinear fourth order kirchhoff type equation. East Asian J. Appl. Math. 8(2), 323\u2013335 (2018)","journal-title":"East Asian J. Appl. Math."},{"key":"1016_CR15","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1016\/j.camwa.2018.03.048","volume":"76","author":"QA Dang","year":"2018","unstructured":"Dang, Q.A., Nguyen, T.H.: Existence results and iterative method for solving a nonlinear biharmonic equation of Kirchhoff type. Comput. Math. Appl. 76, 11\u201322 (2018)","journal-title":"Comput. Math. Appl."},{"issue":"1","key":"1016_CR16","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1016\/j.amc.2018.04.073","volume":"37","author":"QA Dang","year":"2018","unstructured":"Dang, Q.A., Dang, Q.L.: A simple efficient method for solving sixth-order nonlinear boundary value problems. Comp. Appl. Math. 37(1), 16 (2018)","journal-title":"Comp. Appl. Math."},{"key":"1016_CR17","doi-asserted-by":"publisher","first-page":"148","DOI":"10.1007\/s40819-018-0584-9","volume":"4","author":"QA Dang","year":"2018","unstructured":"Dang, Q.A., Nguyen, T.H.: Existence results and numerical method for a fourth order nonlinear problem. Inter. J. Appl. Comput. Math. 4, 148 (2018)","journal-title":"Inter. J. Appl. Comput. Math."},{"key":"1016_CR18","doi-asserted-by":"publisher","first-page":"623","DOI":"10.1007\/s13370-019-00671-6","volume":"30","author":"QA Dang","year":"2019","unstructured":"Dang, Q.A., Nguyen, T.H.: Solving the Dirichlet problem for fully fourth order nonlinear differential equation. Afr. Mat. 30, 623\u2013641 (2019)","journal-title":"Afr. Mat."},{"issue":"10","key":"1016_CR19","first-page":"2244","volume":"13","author":"IH Fazal-I-Haq","year":"2011","unstructured":"Fazal-I-Haq, I.H., Ali, A.: A Haar wavelets based numerical method for third-order boundary and initial value problems. World Appl Sci J 13 (10), 2244\u20132251 (2011)","journal-title":"World Appl Sci J"},{"key":"1016_CR20","doi-asserted-by":"publisher","first-page":"1034","DOI":"10.1016\/j.aml.2004.04.016","volume":"18","author":"Y Feng","year":"2005","unstructured":"Feng, Y., Liu, S.: Solvability of a third-order two-point boundary value problem. Appl. Math. Lett. 18, 1034\u20131040 (2005)","journal-title":"Appl. Math. Lett."},{"issue":"1","key":"1016_CR21","doi-asserted-by":"publisher","first-page":"270","DOI":"10.1016\/j.amc.2005.12.012","volume":"180","author":"F Gao","year":"2006","unstructured":"Gao, F., Chi, C.M.: Solving third-order obstacle problems with quartic B-splines. Appl. Math. Comp. 180(1), 270\u2013274 (2006)","journal-title":"Appl. Math. Comp."},{"key":"1016_CR22","doi-asserted-by":"publisher","first-page":"2407","DOI":"10.1016\/S0362-546X(01)00364-9","volume":"47","author":"MR Grossinho","year":"2001","unstructured":"Grossinho, M.R., Minhos, F.: Existence result for some third order separated boundary value problems. Nonlinear Anal. 47, 2407\u20132418 (2001)","journal-title":"Nonlinear Anal."},{"key":"1016_CR23","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1186\/1687-2770-2012-34","volume":"2012","author":"Y Guo","year":"2012","unstructured":"Guo, Y., Liu, Y., Liang, Y.: Positive solutions for the third-order boundary value problems with the second derivatives. Bound. Value Probl. 2012, 34 (2012)","journal-title":"Bound. Value Probl."},{"issue":"1","key":"1016_CR24","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1016\/j.amc.2004.08.044","volume":"168","author":"S Islam","year":"2007","unstructured":"Islam, S., Khan, M.A., Tirmizi, I.A., Twizell, E.H.: Non-polynomial splines approach to the solution of a system of third-order boundary-value problems. Appl. Math. Comput. 168(1), 152\u2013163 (2007)","journal-title":"Appl. Math. Comput."},{"issue":"2","key":"1016_CR25","doi-asserted-by":"publisher","first-page":"1095","DOI":"10.1016\/j.jmaa.2007.02.046","volume":"335","author":"S Islam","year":"2007","unstructured":"Islam, S., Tirmizi, I.A., Khan, M.A.: Quartic non-polynomial spline approach to the solution of a system of third-order boundary-value problems. J. Math. Anal. Appl. 335(2), 1095\u20131104 (2007)","journal-title":"J. Math. Anal. Appl."},{"key":"1016_CR26","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/S0096-3003(02)00051-6","volume":"137","author":"A Khan","year":"2003","unstructured":"Khan, A., Aziz, T.: The Numerical Solution of Third Order Boundary Value Problems using quintic spline. Appl. Math. Comput. 137, 253\u2013260 (2003)","journal-title":"Appl. Math. Comput."},{"key":"1016_CR27","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1007\/s11075-011-9503-4","volume":"59","author":"A Khan","year":"2012","unstructured":"Khan, A., Sultana, T.: Non-polynomial quintic spline solution for the system of third order boundary-value problems. Numer. Algorithms 59, 541\u2013559 (2012)","journal-title":"Numer. Algorithms"},{"issue":"1","key":"1016_CR28","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1112\/S1461157017000018","volume":"20","author":"X Lv","year":"2017","unstructured":"Lv, X., Gao, J.: Treatment for third-order nonlinear differential equations based on the Adomian decomposition method. LMS J. Comput. Math. 20(1), 1\u201310 (2017)","journal-title":"LMS J. Comput. Math."},{"key":"1016_CR29","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/S0096-3003(03)00632-5","volume":"153","author":"MA Noor","year":"2004","unstructured":"Noor, M.A., Al-Said, E.A.: Quartic spline solutions of third order obstacle boundary value problems. Appl. Math. Comput. 153, 307\u2013316 (2004)","journal-title":"Appl. Math. Comput."},{"key":"1016_CR30","doi-asserted-by":"publisher","first-page":"326","DOI":"10.1186\/s40064-016-1969-z","volume":"5","author":"PK Pandey","year":"2016","unstructured":"Pandey, P.K.: Solving third-order boundary value problems with quartic splines. SpringerPlus 5, 326 (2016)","journal-title":"SpringerPlus"},{"key":"1016_CR31","first-page":"129","volume":"7","author":"PK Pandey","year":"2017","unstructured":"Pandey, P.K.: A numerical method for the solution of general third order boundary value problem in ordinary differential equations. Bull. Inter. Math. Virtual Inst. 7, 129\u2013138 (2017)","journal-title":"Bull. Inter. Math. Virtual Inst."},{"issue":"30","key":"1016_CR32","first-page":"1463","volume":"6","author":"P Pue-on","year":"2012","unstructured":"Pue-on, P., Viriyapong, N.: Modified adomian decomposition method for solving particular third-order ordinary differential equations. Appl. Math. Sci. 6(30), 1463\u20131469 (2012)","journal-title":"Appl. Math. Sci."},{"issue":"1","key":"1016_CR33","first-page":"12","volume":"68","author":"A Rezaiguia","year":"2016","unstructured":"Rezaiguia, A., Kelaiaia, S.: Existence of a positive solution for a third-order three point boundary value problem. Mat. Vesn. 68(1), 12\u201325 (2016)","journal-title":"Mat. Vesn."},{"issue":"6","key":"1016_CR34","doi-asserted-by":"publisher","first-page":"831","DOI":"10.1007\/s11401-012-0749-5","volume":"33","author":"PK Srivastava","year":"2012","unstructured":"Srivastava, P.K., Kumar, M.: Numerical algorithm based on quintic nonpolynomial spline for solving third-order boundary value problems associated with draining and coating flow. Chin. Ann. Math. Ser. B 33(6), 831\u2013840 (2012)","journal-title":"Chin. Ann. Math. Ser. B"},{"key":"1016_CR35","doi-asserted-by":"publisher","first-page":"743","DOI":"10.18514\/MMN.2014.615","volume":"15","author":"Y Sun","year":"2014","unstructured":"Sun, Y., Zhao, M., Li, S.: Monotone positive solution of nonlinear third-order two-point boundary value problem. Miskolc Math. Notes 15, 743\u2013752 (2014)","journal-title":"Miskolc Math. Notes"},{"key":"1016_CR36","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1016\/S0893-9659(01)00122-7","volume":"15","author":"Q Yao","year":"2002","unstructured":"Yao, Q., Feng, Y.: The existence of solutions for a third order two-point boundary value problem. Appl. Math. Lett. 15, 227\u2013232 (2002)","journal-title":"Appl. Math. Lett."},{"key":"1016_CR37","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1186\/s13662-017-1246-7","volume":"2017","author":"C Zhai","year":"2017","unstructured":"Zhai, C., Zhao, L., Li, S., Marasi, H.R.: On some properties of positive solutions for a third-order three-point boundary value problem with a parameter. Adv. Difference Equ. 2017, 187 (2017)","journal-title":"Adv. Difference Equ."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-020-01016-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11075-020-01016-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-020-01016-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T10:44:09Z","timestamp":1698230649000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11075-020-01016-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,7]]},"references-count":37,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,8]]}},"alternative-id":["1016"],"URL":"https:\/\/doi.org\/10.1007\/s11075-020-01016-2","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"type":"print","value":"1017-1398"},{"type":"electronic","value":"1572-9265"}],"subject":[],"published":{"date-parts":[[2020,10,7]]},"assertion":[{"value":"14 July 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 September 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 October 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}