{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T18:01:35Z","timestamp":1770746495400,"version":"3.49.0"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2016,1,19]],"date-time":"2016-01-19T00:00:00Z","timestamp":1453161600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput &amp; Applic"],"published-print":{"date-parts":[[2017,8]]},"DOI":"10.1007\/s00521-016-2185-z","type":"journal-article","created":{"date-parts":[[2016,1,19]],"date-time":"2016-01-19T07:44:33Z","timestamp":1453189473000},"page":"2165-2179","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Biologically inspired computing framework for solving two-point boundary value problems using differential evolution"],"prefix":"10.1007","volume":"28","author":[{"given":"Muhammad Faisal","family":"Fateh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aneela","family":"Zameer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nasir M.","family":"Mirza","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sikander M.","family":"Mirza","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad Asif Zahoor","family":"Raja","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,1,19]]},"reference":[{"key":"2185_CR1","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/0022-0396(70)90106-3","volume":"7","author":"SD Cohen","year":"1970","unstructured":"Cohen SD, Laetsch TW (1970) Nonlinear boundary value problems suggested by chemical reactor theory. J Differ Equ 7:217\u2013226","journal-title":"J Differ Equ"},{"key":"2185_CR2","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1006\/jdeq.1997.3349","volume":"142","author":"K Taira","year":"1998","unstructured":"Taira K, Umezu K (1998) Semilinear elliptic boundary value problems in chemical reactor theory. J Differ Equ 142:434\u2013454","journal-title":"J Differ Equ"},{"key":"2185_CR3","doi-asserted-by":"crossref","first-page":"1237","DOI":"10.1016\/j.mcm.2005.04.008","volume":"42","author":"A Saadatmandi","year":"2005","unstructured":"Saadatmandi A, Razzaghi M, Dehghan M (2005) Sinc-Galerkin solution for nonlinear two-point boundary value problems with applications to chemical reactor theory. Math Comput Model 42:1237\u20131244","journal-title":"Math Comput Model"},{"key":"2185_CR4","doi-asserted-by":"crossref","first-page":"144103","DOI":"10.1063\/1.2052647","volume":"123","author":"A Arnold","year":"2005","unstructured":"Arnold A, Holm C (2005) MMM1D: a method for calculating electrostatic interactions in one-dimensional periodic geometries. J Chem Phys 123:144103","journal-title":"J Chem Phys"},{"key":"2185_CR5","doi-asserted-by":"crossref","first-page":"214103","DOI":"10.1063\/1.2918365","volume":"128","author":"L Levrel","year":"2008","unstructured":"Levrel L, Maggs AC (2008) Boundary conditions in local electrostatics algorithms. J Chem Phys 128:214103","journal-title":"J Chem Phys"},{"key":"2185_CR6","doi-asserted-by":"crossref","first-page":"055109","DOI":"10.1063\/1.3548836","volume":"134","author":"IC Yeh","year":"2011","unstructured":"Yeh IC, Wallqvist A (2011) On the proper calculation of electrostatic interactions in solid-supported bilayer systems. J Chem Phys 134:055109","journal-title":"J Chem Phys"},{"key":"2185_CR7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2009\/260941","volume":"2009","author":"W Cheng","year":"2009","unstructured":"Cheng W, Fu C-L (2009) Solving the axisymmetric inverse heat conduction problem by a wavelet dual least squares method. Bound Value Probl 2009:1\u201313","journal-title":"Bound Value Probl"},{"key":"2185_CR8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2011\/859497","volume":"2011","author":"G Chai","year":"2011","unstructured":"Chai G (2011) Positive solution of fourth-order integral boundary value problem with two parameters. Abstr Appl Anal 2011:1\u201319","journal-title":"Abstr Appl Anal"},{"key":"2185_CR9","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1186\/1687-2770-2011-4","volume":"2011","author":"N Salva","year":"2011","unstructured":"Salva N, Tarzia D, Villa L (2011) An initial-boundary value problem for the one-dimensional non-classical heat equation in a slab. Bound Value Probl 2011:4","journal-title":"Bound Value Probl"},{"key":"2185_CR10","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1093\/imamat\/30.3.247","volume":"30","author":"NHS Haidar","year":"1983","unstructured":"Haidar NHS (1983) Operational analysis of multiregional nuclear reactor kinetics. IMA J Appl Math 30:247\u2013267","journal-title":"IMA J Appl Math"},{"key":"2185_CR11","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1098\/rsif.2005.0092","volume":"3","author":"O Radulescu","year":"2006","unstructured":"Radulescu O, Lagarrigue S, Siegel A, Veber P, Le Borgne M (2006) Topology and static response of interaction networks in molecular biology. J R Soc Interface 3:185\u2013196","journal-title":"J R Soc Interface"},{"key":"2185_CR12","first-page":"1","volume":"2011","author":"Y Zhao","year":"2011","unstructured":"Zhao Y, Sun S, Han Z, Li Q (2011) Positive solutions to boundary value problems of nonlinear fractional differential equations. Abstr Appl Anal 2011:1\u201316","journal-title":"Abstr Appl Anal"},{"key":"2185_CR13","doi-asserted-by":"crossref","first-page":"1677","DOI":"10.1063\/1.1674243","volume":"53","author":"HE Wilhelm","year":"1970","unstructured":"Wilhelm HE (1970) Analysis of nonlinear initial-boundary-value problems in recombination and diffusion kinetics. J Chem Phys 53:1677","journal-title":"J Chem Phys"},{"key":"2185_CR14","doi-asserted-by":"crossref","first-page":"1875","DOI":"10.1063\/1.457092","volume":"91","author":"HM Rabeony","year":"1989","unstructured":"Rabeony HM, Reiss H (1989) Exact solution of boundary value problems involving linear processes of growth and transport in addition polymerization. J Chem Phys 91:1875","journal-title":"J Chem Phys"},{"key":"2185_CR15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2011\/363579","volume":"2011","author":"Y Cao","year":"2011","unstructured":"Cao Y, Yin J, Jin C (2011) A periodic problem of a semilinear pseudoparabolic equation. Abstr Appl Anal 2011:1\u201327","journal-title":"Abstr Appl Anal"},{"key":"2185_CR16","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1186\/1687-2770-2012-88","volume":"2012","author":"M Narayana","year":"2012","unstructured":"Narayana M, Sibanda P, Motsa SS, Siddheshwar PG (2012) On double-diffusive convection and cross diffusion effects on a horizontal wavy surface in a porous medium. Bound Value Probl 2012:88","journal-title":"Bound Value Probl"},{"key":"2185_CR17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2009\/393259","volume":"2009","author":"J Liu","year":"2009","unstructured":"Liu J, Xu W (2009) Positive solutions for some beam equation boundary value problems. Bound Value Probl 2009:1\u20139","journal-title":"Bound Value Probl"},{"key":"2185_CR18","first-page":"1","volume":"2013","author":"J Park","year":"2013","unstructured":"Park J, Bai H, Jang TS (2013) A numerical approach to static deflection analysis of an infinite beam on a nonlinear elastic foundation: one-way spring model. J Appl Math 2013:1\u201310","journal-title":"J Appl Math"},{"key":"2185_CR19","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1186\/1687-2770-2013-154","volume":"2013","author":"J Xie","year":"2013","unstructured":"Xie J, Luo Z (2013) Solutions to a boundary value problem of a fourth-order impulsive differential equation. Bound Value Probl 2013:154","journal-title":"Bound Value Probl"},{"key":"2185_CR20","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1098\/rspa.1990.0029","volume":"428","author":"MS Homer","year":"1990","unstructured":"Homer MS (1990) Boundary value problems for the Laplace tidal wave equation. Proc R Soc A: Math Phys Eng Sci 428:157\u2013180","journal-title":"Proc R Soc A: Math Phys Eng Sci"},{"key":"2185_CR21","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1017\/S002211209300388X","volume":"252","author":"VI Shrira","year":"2006","unstructured":"Shrira VI (2006) Surface waves on shear currents: solution of the boundary-value problem. J Fluid Mech 252:565","journal-title":"J Fluid Mech"},{"key":"2185_CR22","doi-asserted-by":"crossref","first-page":"018903","DOI":"10.1088\/1674-1056\/23\/1\/018903","volume":"23","author":"MAZ Raja","year":"2014","unstructured":"Raja MAZ (2014) Unsupervised neural networks for solving Troesch\u2019s problem. Chin Phys B 23:018903","journal-title":"Chin Phys B"},{"key":"2185_CR23","doi-asserted-by":"crossref","first-page":"860","DOI":"10.1016\/j.ins.2014.04.036","volume":"279","author":"MAZ Raja","year":"2014","unstructured":"Raja MAZ (2014) Stochastic numerical techniques for solving Troesch\u2019s problem. Inf Sci 279:860\u2013873","journal-title":"Inf Sci"},{"key":"2185_CR24","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1080\/09540091.2014.907555","volume":"26","author":"MAZ Raja","year":"2014","unstructured":"Raja MAZ (2014) Solution of one-dimensional Bratu equation arising in the fuel ignition model using ANN optimized with PSO and SQP. Connect Sci 26:195\u2013214","journal-title":"Connect Sci"},{"key":"2185_CR25","doi-asserted-by":"publisher","first-page":"1723","DOI":"10.1007\/s00521-014-1664-3","volume":"25","author":"MAZ Raja","year":"2014","unstructured":"Raja MAZ, Ahmad S-U-I, Samar R (2014) Solution of the 2-dimensional Bratu problem using neural network, swarm intelligence and sequential quadratic programming. Neural Comput Appl 25:1723\u20131739. doi:\n                        10.1007\/s00521-014-1664-3","journal-title":"Neural Comput Appl"},{"key":"2185_CR26","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.neucom.2013.07.013","volume":"124","author":"MAZ Raja","year":"2014","unstructured":"Raja MAZ, Samar R (2014) Numerical treatment for nonlinear MHD Jeffery\u2013Hamel problem using neutral network optimized with interior point algorithm. Neurocomputing 124:178\u2013193","journal-title":"Neurocomputing"},{"key":"2185_CR27","doi-asserted-by":"crossref","first-page":"806","DOI":"10.1016\/j.asoc.2014.08.055","volume":"24","author":"MAZ Raja","year":"2014","unstructured":"Raja MAZ (2014) Numerical treatment for boundary value problems of pantograph functional differential equation using computational intelligence algorithms. Appl Soft Comput 24:806\u2013821","journal-title":"Appl Soft Comput"},{"key":"2185_CR28","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.compfluid.2013.12.005","volume":"91","author":"MAZ Raja","year":"2014","unstructured":"Raja MAZ (2014) Numerical treatment of nonlinear MHD Jeffery\u2013Hamel problems using stochastic algorithms. Comput Fluids 91:28\u201346","journal-title":"Comput Fluids"},{"key":"2185_CR29","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1016\/j.asoc.2014.10.009","volume":"26","author":"MAZ Raja","year":"2015","unstructured":"Raja MAZ, Khan JA, Behloul D, Haroon T, Siddiqui AM, Samar R (2015) Exactly satisfying initial conditions neural network models for numerical treatment of first Painleve equation. Appl Soft Comput 26:244\u2013256","journal-title":"Appl Soft Comput"},{"key":"2185_CR30","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/j.asoc.2009.07.006","volume":"10","author":"HS Yazdi","year":"2010","unstructured":"Yazdi HS, Pourreza R (2010) Unsupervised adaptive neural-fuzzy inference system for solving differential equations. Appl Soft Comput 10:267\u2013275","journal-title":"Appl Soft Comput"},{"key":"2185_CR31","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.asoc.2008.02.003","volume":"9","author":"Y Shirvany","year":"2009","unstructured":"Shirvany Y, Hayati M, Moradian R (2009) Multilayer perceptron neural networks with novel unsupervised training method for numerical solution of the partial differential equations. Appl Soft Comput 9:20\u201329","journal-title":"Appl Soft Comput"},{"key":"2185_CR32","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1109\/TEVC.2007.908467","volume":"12","author":"A Sobester","year":"2008","unstructured":"Sobester A, Nair PB, Keane AJ (2008) Genetic programming approaches for solving elliptic partial differential equations. IEEE Trans Evol Comput 12:469\u2013478","journal-title":"IEEE Trans Evol Comput"},{"key":"2185_CR33","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/s10710-006-7009-y","volume":"7","author":"IG Tsoulos","year":"2006","unstructured":"Tsoulos IG, Lagaris IE (2006) Solving differential equations with genetic programming. Genet Program Evolvable Mach 7:33\u201354","journal-title":"Genet Program Evolvable Mach"},{"key":"2185_CR34","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.anucene.2013.10.024","volume":"65","author":"A Zameer","year":"2013","unstructured":"Zameer A, Mirza SM, Mirza NM (2013) Core loading pattern optimization of a typical two-loop 300\u00a0MWe PWR using Simulated Annealing (SA), novel crossover Genetic Algorithms (GA) ahd hybrid GA (SA) schemes. Ann Nucl Energy 65:122\u2013131","journal-title":"Ann Nucl Energy"},{"key":"2185_CR35","doi-asserted-by":"crossref","first-page":"2809","DOI":"10.12785\/amis\/080617","volume":"8","author":"ZS Abo-Hammour","year":"2014","unstructured":"Abo-Hammour ZS, Arqub OA, Alsmadi O, Momani S, Alsaedi A (2014) An optimization algorithm for solving systems of singular boundary value problems. Appl Math Inf Sci 8:2809\u20132821","journal-title":"Appl Math Inf Sci"},{"key":"2185_CR36","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/401696","author":"ZS Abo-Hammour","year":"2014","unstructured":"Abo-Hammour ZS, Arqub OA, Momani S, Shawagfeh N (2014) Optimization solution of Troesch\u2019s and Bratu\u2019s problems of ordinary type using novel continuous genetic algorithm. Discrete Dyn Nat Soc. doi:\n                        10.1155\/2014\/401696","journal-title":"Discrete Dyn Nat Soc"},{"key":"2185_CR37","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1016\/j.ins.2014.03.128","volume":"279","author":"OA Arqub","year":"2014","unstructured":"Arqub OA, Abo-Hammour ZS (2014) Numerical solution of systems of second-order boundary value problems using continuous genetic algorithm. Inf Sci 279:396\u2013415","journal-title":"Inf Sci"},{"key":"2185_CR38","doi-asserted-by":"crossref","first-page":"235","DOI":"10.12785\/amis\/080129","volume":"8","author":"OA Arqub","year":"2014","unstructured":"Arqub OA, Abo-Hammour ZS, Momani S (2014) Application of continuous genetic algorithm for nonlinear system of second-order boundary value problems. Appl Math Inf Sci 8:235\u2013248","journal-title":"Appl Math Inf Sci"},{"key":"2185_CR39","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/205391","author":"OA Arqub","year":"2012","unstructured":"Arqub OA, Abo-Hammour ZS, Momani S, Shawagfeh N (2012) Solving singular two-point boundary value problems using continuous genetic algorithm. Abstr Appl Anal. doi:\n                        10.1155\/2012\/205391","journal-title":"Abstr Appl Anal"},{"key":"2185_CR40","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-014-9701-9","author":"Y Xu","year":"2014","unstructured":"Xu Y, Fang J, Zhu W, Wang X, Zhao L (2014) Differential evolution using superior-inferior crossover scheme. Comput Optim Appl. doi:\n                        10.1007\/s10589-014-9701-9","journal-title":"Comput Optim Appl"},{"key":"2185_CR41","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1007\/s10589-012-9521-8","volume":"55","author":"MH Kashan","year":"2013","unstructured":"Kashan MH, Kashan AH, Nahavandi N (2013) A novel differential evolution algorithm for binary optimization. Comput Optim Appl 55:481\u2013513","journal-title":"Comput Optim Appl"},{"key":"2185_CR42","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1007\/s10589-012-9498-3","volume":"54","author":"MM Ali","year":"2013","unstructured":"Ali MM, Zhu WX (2013) A penalty function-based differential evolution algorithm for constrained global optimization. Comput Optim Appl 54:707\u2013739","journal-title":"Comput Optim Appl"},{"key":"2185_CR43","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1023\/A:1008202821328","volume":"11","author":"R Storn","year":"1997","unstructured":"Storn R, Price K (1997) Differential evolution: a simple and efficient adaptive scheme for global optimization over continuous spaces. J Glob Optim 11:341\u2013359","journal-title":"J Glob Optim"},{"key":"2185_CR44","doi-asserted-by":"crossref","first-page":"1219","DOI":"10.1002\/nme.1108","volume":"61","author":"ZS Abo-Hammour","year":"2004","unstructured":"Abo-Hammour ZS, Yusuf M, Mirza NM, Mirza SM, Arif M, Khurshid J (2004) Numerical solution of second-order, two-point boundary value problems using continuous genetic algorithms. Int J Numer Methods Eng 61:1219\u20131242","journal-title":"Int J Numer Methods Eng"},{"key":"2185_CR45","doi-asserted-by":"crossref","unstructured":"Yang M, Cai Z, Li C, Guan J (2013) An improved adaptive differential evolution algorithm with population adaptation. Genet Evol Comput Conf, Copyright 2013 ACM 978-1-4503-1963-8\/13\/07, Amsterdam, pp 145\u2013152","DOI":"10.1145\/2463372.2463374"},{"key":"2185_CR46","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/s10462-009-9137-2","volume":"33","author":"F Neri","year":"2010","unstructured":"Neri F, Tirronen V (2010) Recent advances in differential evolution: a survey and experimental analysis. Artif Intell Rev 33:61\u2013106","journal-title":"Artif Intell Rev"},{"key":"2185_CR47","first-page":"4921","volume":"6","author":"CK Tat","year":"2012","unstructured":"Tat CK, Majid ZA, Suleiman M, Senu N (2012) Solving linear two-point boundary value problems by Direct Adams Moulton method. Appl Math Sci 6:4921\u20134929","journal-title":"Appl Math Sci"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00521-016-2185-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-016-2185-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-016-2185-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-016-2185-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T02:21:28Z","timestamp":1559096488000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00521-016-2185-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1,19]]},"references-count":47,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2017,8]]}},"alternative-id":["2185"],"URL":"https:\/\/doi.org\/10.1007\/s00521-016-2185-z","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,1,19]]}}}