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To evaluate the performance of the proposed method, numerical examples are performed by the presented method. Comparison of the numerical results with exact solutions validate the feasibility of the proposed method in accuracy. Results compared with other recent research works also validate the superiority of the proposed approach. Numerical results show that the proposed BNN with IELM algorithm perform well in accuracy and requires less hidden neurons.<\/jats:p>","DOI":"10.3233\/jifs-190406","type":"journal-article","created":{"date-parts":[[2019,12,20]],"date-time":"2019-12-20T11:48:58Z","timestamp":1576842538000},"page":"3445-3461","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":10,"title":["Numerical solution of several kinds of differential equations using block neural network method with improved extreme learning machine algorithm"],"prefix":"10.1177","volume":"38","author":[{"given":"Yunlei","family":"Yang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Guizhou University, Guiyang, China"}]},{"given":"Muzhou","family":"Hou","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Central South University, Changsha, China"}]},{"given":"Jianshu","family":"Luo","sequence":"additional","affiliation":[{"name":"High-tech Research Institute, Hunan Institute of Traffic Engineering, Hengyang, China"}]},{"given":"Zhongchu","family":"Tian","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Changsha University of Science and Technology, Changsha, China"}]}],"member":"179","published-online":{"date-parts":[[2019,12,18]]},"reference":[{"key":"e_1_3_2_2_2","unstructured":"K.S.Mcfall An artificial neural network method for solving boundary value problems with arbitrary irregular boundaries Ph.D. thesis Georgia Institute of Technology (2006)."},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2007.04.024"},{"key":"e_1_3_2_4_2","doi-asserted-by":"crossref","unstructured":"N.Yadav A.Yadav and K.Deep Artificial neural network technique for solution of nonlinear elliptic boundary value problems in Proceedings of Fourth International Conference on Soft Computing for Problem Solving Advances in Intelligent Systems and Computing 335 (2015) 113\u2013121.","DOI":"10.1007\/978-81-322-2217-0_10"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2008.12.004"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2010.11.015"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2011.09.028"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2010.01.005"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2009.05.003"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2008.01.017"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-81-322-0487-9_3"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2013.07.016"},{"key":"e_1_3_2_13_2","doi-asserted-by":"crossref","unstructured":"N.Yadav A.Yadav and M.Kumar An introduction to neural network methods for differential equations Springer Netherlands (2015).","DOI":"10.1007\/978-94-017-9816-7"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2018.07.010"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11063-017-9761-9"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2018.05.028"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-6080(05)80131-5"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11587-018-0384-x"},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2005.12.126"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2006.875977"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2007.02.009"},{"key":"e_1_3_2_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2007.10.008"},{"key":"e_1_3_2_23_2","doi-asserted-by":"publisher","DOI":"10.1109\/TSMCB.2011.2168604"},{"key":"e_1_3_2_24_2","first-page":"1","article-title":"Kernel-based multilayer extreme learning machines for representation learning","volume":"99","author":"Wong C.M.","year":"2016","unstructured":"C.M.Wong, C.M.Vong, P.K.Wong, et al., Kernel-based multilayer extreme learning machines for representation learning, IEEE Transactions on Neural Networks & Learning Systems 99 (2016), 1\u20136.","journal-title":"IEEE Transactions on Neural Networks & Learning Systems"},{"key":"e_1_3_2_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2012.07.015"},{"key":"e_1_3_2_26_2","unstructured":"E.Suli Finite element methods for partial differential equations. 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