{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:42:25Z","timestamp":1777704145206,"version":"3.51.4"},"reference-count":46,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2019,12,7]],"date-time":"2019-12-07T00:00:00Z","timestamp":1575676800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2020,3,4]]},"abstract":"<jats:p>\u00a0This research paper studies the computational and numerical solutions of the transmission of nerve impulses of a nervous system (the neuron) by applying the modified Khater (mK) method and B-spline scheme to the FitzHugh-Nagumo (FN) equation where it is usually used as a model of the transmission of nerve impulses. This study focuses on finding the different types of soliton wave solutions, studying the stability property of them, and then use them to obtain the numerical solutions of the model. The obtained solutions are compared with each other to show the absolute value of error between them that will explain the accuracy of both types of solutions. Moreover, in the text of more explanation of the physical properties of the suggested model, some sketches are plotted. Also, the performance of both techniques is investigated to show its ability for applying to other nonlinear evolutions equation.<\/jats:p>","DOI":"10.3233\/jifs-179547","type":"journal-article","created":{"date-parts":[[2019,12,10]],"date-time":"2019-12-10T11:11:52Z","timestamp":1575976312000},"page":"2603-2610","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":7,"title":["On the computational and numerical solutions of the transmission of nerve impulses of an excitable system (the neuron system)"],"prefix":"10.1177","volume":"38","author":[{"given":"Mostafa M.A.","family":"Khater","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Jiangsu University, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Raghda A.M.","family":"Attia","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Jiangsu University, China"},{"name":"Department of Basic Science, Higher Technological Institute 10th of Ramadan city, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abdel-Haleem","family":"Abdel-Aty","sequence":"additional","affiliation":[{"name":"Department of Physics, College of Sciences, University of Bisha, Bisha, Saudi Arabia"},{"name":"Physics Department, Faculty of Science, Al-Azhar University, Assiut, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sayed","family":"Abdel-Khalek","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yas","family":"Al-Hadeethi","sequence":"additional","affiliation":[{"name":"Department of Physics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dianchen","family":"Lu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Jiangsu University, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2019,12,7]]},"reference":[{"key":"e_1_3_2_2_2","volume-title":"Fractional Differential Equations, Mathematics in Science and Engineering","author":"Podlubny I.","year":"1999","unstructured":"I.Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, San Diego, CA: Academic Press, 1999."},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1088\/0253-6102\/71\/9\/1063"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2019.109395"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-018-28607-3"},{"key":"e_1_3_2_6_2","first-page":"31","article-title":"Fractional complex transform for space-time fractional nonlinear differential equations arising in plasma physics","volume":"5","author":"Abdou M.A.","year":"2014","unstructured":"M.A.Abdou, A.Elgarayhi and E.El-Shewy, Fractional complex transform for space-time fractional nonlinear differential equations arising in plasma physics, Nonlinear Sci Lett A 5 (2014), 31\u201334.","journal-title":"Nonlinear Sci Lett A"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1088\/1402-4896\/ab156b"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218348X19400103"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2019084"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1088\/1555-6611\/ab02f9"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00033-019-1107-1"},{"key":"e_1_3_2_12_2","doi-asserted-by":"crossref","unstructured":"G.Arioli and K.Hans Traveling wave solutions for the FPU chain: A constructive approach. arXiv preprint arXiv:1903.01299 2019.","DOI":"10.1088\/1361-6544\/ab6a78"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2018.10.012"},{"key":"e_1_3_2_14_2","unstructured":"L.-C.Hung and L.Xian Nonlinear estimates for traveling wave solutions of reaction diffusion equations. arXiv preprint arXiv:1907.05821 2019."},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00332-018-9510-x"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2019.124576"},{"key":"e_1_3_2_17_2","unstructured":"E.Carrera M.Cinefra A.Pagani M.Petrolo and E.Zappino Numerical Simulation Of Fluidic Thrust-Vectoring 2019."},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.95.032123"},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.3934\/dcdss.2019058"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.1088\/1402-4896\/aa6630"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.pquantelec.2007.03.002"},{"key":"e_1_3_2_22_2","doi-asserted-by":"publisher","DOI":"10.1113\/jphysiol.1952.sp004764"},{"key":"e_1_3_2_23_2","doi-asserted-by":"publisher","DOI":"10.1239\/aap\/1282924062"},{"key":"e_1_3_2_24_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02477753"},{"key":"e_1_3_2_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0006-3495(61)86902-6"},{"key":"e_1_3_2_26_2","unstructured":"R.FitzHugh Mathematical models of excitation and propagation in nerve Biological Engineering (1969) 1\u201385."},{"key":"e_1_3_2_27_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.5050178"},{"key":"e_1_3_2_28_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-019-2115-3"},{"key":"e_1_3_2_29_2","first-page":"27","article-title":"Numerical method for homoclinic and heteroclinic orbits of neuron models","volume":"1","author":"Deng B.","year":"2019","unstructured":"B.Deng, Numerical method for homoclinic and heteroclinic orbits of neuron models, Journal of Nonlinear Modeling and Analysis 1 (2019), 27\u201345. Website: http:\/\/jnma.ca1.","journal-title":"Journal of Nonlinear Modeling and Analysis"},{"key":"e_1_3_2_30_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40314-016-0406-9"},{"issue":"9","key":"e_1_3_2_31_2","article-title":"Dynamic transitions of the fitzhugh-nagumo equations On a finite domain","volume":"23","author":"Mao Y.","year":"2018","unstructured":"Y.Mao, Dynamic transitions of the fitzhugh-nagumo equations On a finite domain, Discrete & Continuous Dynamical Systems-Series B 23(9) (2018).","journal-title":"Discrete & Continuous Dynamical Systems-Series B"},{"key":"e_1_3_2_32_2","doi-asserted-by":"crossref","unstructured":"H.Rezazadeh A.Korkmaz M.M.A.Khater M.Eslami D.Lu and R.A.M.Attia New exact traveling wave solutions of biological population model via the extended rational sinh-cosh method and the modified Khater method Modern Physics Letters B (2019) 1950338.","DOI":"10.1142\/S021798491950338X"},{"key":"e_1_3_2_33_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.5087647"},{"key":"e_1_3_2_34_2","doi-asserted-by":"crossref","unstructured":"M.M.A.Khater D.Lu and R.A.M.Attia Lump soliton wave solutions for the (2+ 1)-dimensional Konopelchenko\u2013Dubrovsky equation and KdV equation Modern Physics Letters B (2019) 1950199.","DOI":"10.1142\/S0217984919501999"},{"key":"e_1_3_2_35_2","doi-asserted-by":"publisher","DOI":"10.3390\/mca24010010"},{"key":"e_1_3_2_36_2","doi-asserted-by":"publisher","DOI":"10.3390\/e21040397"},{"key":"e_1_3_2_37_2","unstructured":"R.P.Merges The Hamiltonian Origins of the US Patent System and Why They Matter Today. Iowa Law Review Forthcoming 2019."},{"key":"e_1_3_2_38_2","doi-asserted-by":"publisher","DOI":"10.1201\/9780203750087"},{"key":"e_1_3_2_39_2","doi-asserted-by":"publisher","DOI":"10.1080\/03081087.2017.1415292"},{"key":"e_1_3_2_40_2","doi-asserted-by":"publisher","DOI":"10.1029\/2018GL080931"},{"key":"e_1_3_2_41_2","doi-asserted-by":"publisher","DOI":"10.1201\/9780203750087"},{"key":"e_1_3_2_42_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.joes.2019.03.002"},{"key":"e_1_3_2_43_2","doi-asserted-by":"publisher","DOI":"10.1080\/25765299.2019.1628687"},{"key":"e_1_3_2_44_2","doi-asserted-by":"crossref","unstructured":"R.Mohammadi Numerical approximation for viscous Cahn\u2013Hilliard equation via septic B-spline Applicable Analysis (2019) 1\u201323.","DOI":"10.1080\/00036811.2019.1594200"},{"key":"e_1_3_2_45_2","doi-asserted-by":"publisher","DOI":"10.1080\/16583655.2019.1617986"},{"issue":"3","key":"e_1_3_2_46_2","first-page":"319","article-title":"A numerical study using finite element method for generalized Rosenau-Kawahara-RLW equation","volume":"7","author":"Karakoc G.","year":"2019","unstructured":"G.Karakoc, S.Battal, S.K.Bhowmik and F.Gao, A numerical study using finite element method for generalized Rosenau-Kawahara-RLW equation, Computational Methods for Differential Equations 7(3) (2019), 319\u2013333.","journal-title":"Computational Methods for Differential Equations"},{"key":"e_1_3_2_47_2","doi-asserted-by":"publisher","DOI":"10.5120\/19955-1791"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-179547","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-179547","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-179547","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:40:32Z","timestamp":1777455632000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-179547"}},"subtitle":[],"editor":[{"given":"Ahmed","family":"Farouk","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2019,12,7]]},"references-count":46,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,3,4]]}},"alternative-id":["10.3233\/JIFS-179547"],"URL":"https:\/\/doi.org\/10.3233\/jifs-179547","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,12,7]]}}}