{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T19:20:22Z","timestamp":1772133622669,"version":"3.50.1"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2015,9,1]],"date-time":"2015-09-01T00:00:00Z","timestamp":1441065600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"BK21 and NRF","award":["NRF- 2013R1A2A1A01013886"],"award-info":[{"award-number":["NRF- 2013R1A2A1A01013886"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput & Applic"],"published-print":{"date-parts":[[2017,1]]},"DOI":"10.1007\/s00521-015-2046-1","type":"journal-article","created":{"date-parts":[[2015,8,31]],"date-time":"2015-08-31T05:26:05Z","timestamp":1440998765000},"page":"171-178","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":39,"title":["An efficient algorithm based on artificial neural networks and particle swarm optimization for solution of nonlinear Troesch\u2019s problem"],"prefix":"10.1007","volume":"28","author":[{"given":"Neha","family":"Yadav","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anupam","family":"Yadav","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Manoj","family":"Kumar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joong Hoon","family":"Kim","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,9,1]]},"reference":[{"key":"2046_CR1","first-page":"60","volume-title":"The plasma in a magnetic field","author":"ES Weibel","year":"1958","unstructured":"Weibel ES (1958) Confinement of a plasma column by radiation pressure. In: Landshoff RKM (ed) The plasma in a magnetic field. Stanford University Press, Stanford, pp 60\u201376"},{"issue":"3","key":"2046_CR2","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/0021-9991(76)90026-7","volume":"21","author":"SM Roberts","year":"1976","unstructured":"Roberts SM, Shipmann J (1976) On the closed form solution of Troesch\u2019s problem. J Comput Phys 21(3):291\u2013304","journal-title":"J Comput Phys"},{"key":"2046_CR3","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/B978-0-12-068660-5.50008-9","volume-title":"Numerical solutions of boundary value problems for ordinary differential equations","author":"MR Scott","year":"1975","unstructured":"Scott MR (1975) On the conversion of boundary value problems into stable initial value problems via several invariant imbedding algorithms. In: Aziz AK (ed) Numerical solutions of boundary value problems for ordinary differential equations. Academic Press, New York, pp 89\u2013146"},{"issue":"4","key":"2046_CR4","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1080\/0020716022000009228","volume":"80","author":"SA Khuri","year":"2003","unstructured":"Khuri SA (2003) A numerical algorithm for solving the Troesch\u2019s problem. Int J Comput Math 80(4):493\u2013498","journal-title":"Int J Comput Math"},{"issue":"1","key":"2046_CR5","doi-asserted-by":"crossref","first-page":"500","DOI":"10.1016\/j.amc.2006.11.161","volume":"189","author":"X Feng","year":"2007","unstructured":"Feng X, Mei L, He G (2007) An efficient algorithm for solving Troesch\u2019s problem. Appl Math Comput 189(1):500\u2013507","journal-title":"Appl Math Comput"},{"issue":"2","key":"2046_CR6","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1016\/j.amc.2007.05.026","volume":"195","author":"SH Chang","year":"2008","unstructured":"Chang SH, Chang IL (2008) A new algorithm for calculating the one dimensional differential transform of non linear functions. Appl Math Comput 195(2):799\u2013808","journal-title":"Appl Math Comput"},{"issue":"10","key":"2046_CR7","doi-asserted-by":"crossref","first-page":"3043","DOI":"10.1016\/j.cam.2010.04.018","volume":"234","author":"SH Chang","year":"2010","unstructured":"Chang SH (2010) A variational iteration method for solving Troesch\u2019s problem. J Comput Appl Math 234(10):3043\u20133047","journal-title":"J Comput Appl Math"},{"issue":"11","key":"2046_CR8","doi-asserted-by":"crossref","first-page":"3303","DOI":"10.1016\/j.amc.2010.04.056","volume":"216","author":"SH Chang","year":"2010","unstructured":"Chang SH (2010) Numerical solution of Troesch\u2019s problem by simple shooting method. Appl Math Comput 216(11):3303\u20133306","journal-title":"Appl Math Comput"},{"issue":"9\u201310","key":"2046_CR9","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1016\/j.mcm.2011.11.071","volume":"56","author":"M Zarebnia","year":"2012","unstructured":"Zarebnia M, Sajjadian M (2012) The sinc-Galerkin method for solving Troesch\u2019s problem. Math Comput Model 56(9\u201310):218\u2013228","journal-title":"Math Comput Model"},{"key":"2046_CR10","doi-asserted-by":"crossref","unstructured":"Vazquez-Leal H, Khan Y, Fernandez-Anaya G et al (2012) A general solution for Troesch\u2019s problem. Math Probl Eng, Article ID 208375","DOI":"10.1155\/2012\/208375"},{"issue":"9\u201310","key":"2046_CR11","doi-asserted-by":"crossref","first-page":"1907","DOI":"10.1016\/j.mcm.2011.04.030","volume":"54","author":"SA Khuri","year":"2011","unstructured":"Khuri SA, Sayfy A (2011) Troesch\u2019s problem: a B-spline collocation approach. Math Comput Model 54(9\u201310):1907\u20131918","journal-title":"Math Comput Model"},{"issue":"10","key":"2046_CR12","doi-asserted-by":"crossref","first-page":"2132","DOI":"10.1016\/j.cnsns.2007.04.024","volume":"13","author":"Y Shirvany","year":"2008","unstructured":"Shirvany Y, Hayati M, Moradian R (2008) Numerical solution of the nonlinear Schrodinger equation by feedforward neural networks. Commun Nonlinear Sci Numer Simul 13(10):2132\u20132145","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"2046_CR13","doi-asserted-by":"crossref","first-page":"1942","DOI":"10.1109\/ICNN.1995.488968","volume":"4","author":"J Kennedy","year":"1995","unstructured":"Kennedy J, Mendes R (1995) Particle swarm optimization. Proc IEEE Int Conf Neural Netw 4:1942\u20131948","journal-title":"Proc IEEE Int Conf Neural Netw"},{"key":"2046_CR14","first-page":"1895","volume":"2","author":"R Mendes","year":"2002","unstructured":"Mendes R, Cortez P, Rocha M, Neves J (2002) Particle swarms for feed forward neural network training. Proc Int Jt Conf Neural Netw 2:1895\u20131899","journal-title":"Proc Int Jt Conf Neural Netw"},{"issue":"1","key":"2046_CR15","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1016\/j.amc.2013.05.065","volume":"220","author":"A Yadav","year":"2013","unstructured":"Yadav A, Deep K (2013) Shrinking hypersphere based trajectory of particles in PSO. Appl Math Comput 220(1):246\u2013267","journal-title":"Appl Math Comput"},{"issue":"4","key":"2046_CR16","first-page":"514","volume":"34","author":"JA Khan","year":"2009","unstructured":"Khan JA, Zahoor RMA, Qureshi IM (2009) Swarm intelligence for the problems of non-linear ordinary differential equations and its application to well known Wessinger\u2019s equation. Eur J Sci Res 34(4):514\u2013525","journal-title":"Eur J Sci Res"},{"issue":"7\u20138","key":"2046_CR17","doi-asserted-by":"crossref","first-page":"1507","DOI":"10.1007\/s00521-014-1661-6","volume":"25","author":"AR Jordehi","year":"2014","unstructured":"Jordehi AR (2014) Particle swarm optimization for dynamic optimization problems: a review. Neural Comput Appl 25(7\u20138):1507\u20131516","journal-title":"Neural Comput Appl"},{"issue":"2","key":"2046_CR18","doi-asserted-by":"crossref","first-page":"1026","DOI":"10.1016\/j.amc.2006.07.025","volume":"185","author":"JR Jhang","year":"2007","unstructured":"Jhang JR, Zhang J, Lok TM, Lyu MR (2007) A hybrid particle swarm optimization-back propagation algorithm for feed forward neural network training. Appl Math Comput 185(2):1026\u20131037","journal-title":"Appl Math Comput"},{"issue":"10\u201312","key":"2046_CR19","doi-asserted-by":"crossref","first-page":"2385","DOI":"10.1016\/j.neucom.2008.12.004","volume":"72","author":"IG Tsoulos","year":"2009","unstructured":"Tsoulos IG, Gavrilis D, Glavas E (2009) Solving differential equations with constructed neural networks. Neurocomputing 72(10\u201312):2385\u20132391","journal-title":"Neurocomputing"},{"issue":"1","key":"2046_CR20","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1109\/4235.985692","volume":"6","author":"M Clerc","year":"2002","unstructured":"Clerc M, Kennedy J (2002) The particle swarm-explosion, stability and convergence in a multidimensional complex space. IEEE Trans Evol Comput 6(1):58\u201373","journal-title":"IEEE Trans Evol Comput"},{"issue":"2","key":"2046_CR21","doi-asserted-by":"crossref","first-page":"618","DOI":"10.1016\/j.asoc.2009.08.029","volume":"10","author":"MEH Pedersen","year":"2010","unstructured":"Pedersen MEH, Chipperfield AJ (2010) Simplifying particle swarm optimization. Appl Soft Comput 10(2):618\u2013628","journal-title":"Appl Soft Comput"},{"issue":"3","key":"2046_CR22","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/0021-9991(76)90025-5","volume":"21","author":"BA Troesch","year":"1976","unstructured":"Troesch BA (1976) A simple approach to a sensitive two-point boundary value problem. J Comput Phys 21(3):279\u2013290","journal-title":"J Comput Phys"},{"issue":"5","key":"2046_CR23","doi-asserted-by":"crossref","first-page":"987","DOI":"10.1109\/72.712178","volume":"9","author":"IE Lagaris","year":"1998","unstructured":"Lagaris IE, Likas A (1998) Artificial neural networks for solving ordinary and partial differential equations. IEEE Trans Neural Networks 9(5):987\u20131000","journal-title":"IEEE Trans Neural Networks"},{"issue":"1","key":"2046_CR24","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1016\/j.amc.2006.05.068","volume":"183","author":"A Malek","year":"2006","unstructured":"Malek A, Shekari Beidokhti R (2006) Numerical solution for high order differential equations using a hybrid neural network\u2014optimization method. Appl Math Comput 183(1):260\u2013271","journal-title":"Appl Math Comput"},{"issue":"8","key":"2046_CR25","doi-asserted-by":"crossref","first-page":"1221","DOI":"10.1109\/TNN.2009.2020735","volume":"20","author":"KS McFall","year":"2009","unstructured":"McFall KS, Mahan JR (2009) Artificial neural network method for solution of boundary value problems with exact satisfaction of arbitrary boundary conditions. IEEE Trans Neural Networks 20(8):1221\u20131233","journal-title":"IEEE Trans Neural Networks"},{"issue":"10","key":"2046_CR26","doi-asserted-by":"crossref","first-page":"3796","DOI":"10.1016\/j.camwa.2011.09.028","volume":"62","author":"M Kumar","year":"2011","unstructured":"Kumar M, Yadav N (2011) Multilayer perceptrons and radial basis function neural network methods for the solution of differential equations: a survey. Comput Math Appl 62(10):3796\u20133811","journal-title":"Comput Math Appl"},{"issue":"5","key":"2046_CR27","doi-asserted-by":"crossref","first-page":"1041","DOI":"10.1109\/72.870037","volume":"11","author":"IE Lagaris","year":"2000","unstructured":"Lagaris IE, Likas A, Papageorgiou DG (2000) Neural network methods for boundary value problems with irregular boundaries. IEEE Trans Neural Netw 11(5):1041\u20131049","journal-title":"IEEE Trans Neural Netw"},{"issue":"2","key":"2046_CR28","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1016\/j.jfranklin.2012.11.003","volume":"350","author":"KS Mcfall","year":"2013","unstructured":"Mcfall KS (2013) Automated design parameter selection for neural networks solving coupled partial differential equations with discontinuities. J Frankl Inst 350(2):300\u2013317","journal-title":"J Frankl Inst"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-015-2046-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00521-015-2046-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-015-2046-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-015-2046-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,21]],"date-time":"2022-05-21T03:51:41Z","timestamp":1653105101000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00521-015-2046-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,9,1]]},"references-count":28,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,1]]}},"alternative-id":["2046"],"URL":"https:\/\/doi.org\/10.1007\/s00521-015-2046-1","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,9,1]]}}}