{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T13:54:56Z","timestamp":1764078896242,"version":"3.41.2"},"reference-count":30,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,5,16]],"date-time":"2012-05-16T00:00:00Z","timestamp":1337126400000},"content-version":"vor","delay-in-days":136,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>Mathematical form for two energy groups of three\u2010dimensional homogeneous reactor kinetics equations and average one group of the precursor concentration of delayed neutrons is presented. This mathematical form is called \u201ctwo energy groups of the point kinetics equations.\u201d We rewrite two energy groups of the point kinetics equations in the matrix form. Generalization of the analytical exponential model (GAEM) is developed for solving two energy groups of the point kinetics equations. The GAEM is based on the eigenvalues and the corresponding eigenvectors of the coefficient matrix. The eigenvalues of the coefficient matrix are calculated numerically using visual FORTRAN code, based on Laguerre\u2019s method, to calculate the roots of an algebraic equation with real coefficients. The eigenvectors of the coefficient matrix are calculated analytically. The results of the GAEM are compared with the traditional methods. These comparisons substantiate the accuracy of the results of the GAEM. In addition, the GAEM is faster than the traditional methods.<\/jats:p>","DOI":"10.1155\/2012\/282367","type":"journal-article","created":{"date-parts":[[2012,5,17]],"date-time":"2012-05-17T12:25:04Z","timestamp":1337257504000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Generalization of the Analytical Exponential Model for Homogeneous Reactor Kinetics Equations"],"prefix":"10.1155","volume":"2012","author":[{"given":"Abdallah A.","family":"Nahla","sequence":"first","affiliation":[]},{"given":"Mohammed F.","family":"Al-Ghamdi","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,5,16]]},"reference":[{"key":"e_1_2_6_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0306-4549(00)00089-X"},{"key":"e_1_2_6_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.anucene.2005.01.011"},{"key":"e_1_2_6_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.anucene.2005.05.003"},{"key":"e_1_2_6_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.pnucene.2006.11.003"},{"key":"e_1_2_6_5_2","doi-asserted-by":"publisher","DOI":"10.1080\/18811248.2002.9715234"},{"key":"e_1_2_6_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0306-4549(01)00103-7"},{"key":"e_1_2_6_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2010.03.020"},{"key":"e_1_2_6_8_2","doi-asserted-by":"publisher","DOI":"10.1080\/18811248.2003.9715350"},{"key":"e_1_2_6_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.anucene.2009.12.011"},{"key":"e_1_2_6_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.anucene.2005.11.003"},{"key":"e_1_2_6_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.anucene.2006.07.012"},{"key":"e_1_2_6_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.anucene.2007.10.008"},{"key":"e_1_2_6_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.pnucene.2008.10.003"},{"key":"e_1_2_6_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.anucene.2010.02.005"},{"key":"e_1_2_6_15_2","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/35\/14\/307"},{"key":"e_1_2_6_16_2","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/35\/45\/309"},{"key":"e_1_2_6_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0306-4549(03)00033-1"},{"key":"e_1_2_6_18_2","doi-asserted-by":"publisher","DOI":"10.13182\/NSE89-A23663"},{"key":"e_1_2_6_19_2","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/39\/8\/006"},{"key":"e_1_2_6_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.nucengdes.2008.04.002"},{"key":"e_1_2_6_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.anucene.2008.11.005"},{"key":"e_1_2_6_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.nucengdes.2010.03.003"},{"volume-title":"Dynamics of Nuclear Reactors","year":"1993","author":"Hetrick D. 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