{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T04:29:10Z","timestamp":1779337750017,"version":"3.51.4"},"reference-count":0,"publisher":"Informa UK Limited","issue":"2","license":[{"start":{"date-parts":[[1999,1,1]],"date-time":"1999-01-01T00:00:00Z","timestamp":915148800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics and Decision Sciences"],"published-print":{"date-parts":[[1999,1,1]]},"abstract":"<jats:p>Nagumo's equation is a third order non-linear ordinary differential equation\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mfrac><mml:mrow><mml:msup><mml:mi>d<\/mml:mi><mml:mn>3<\/mml:mn><\/mml:msup><mml:mi>u<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>d<\/mml:mi><mml:msup><mml:mi>x<\/mml:mi><mml:mn>3<\/mml:mn><\/mml:msup><\/mml:mrow><\/mml:mfrac><mml:mo>\u2212<\/mml:mo><mml:mi>c<\/mml:mi><mml:mfrac><mml:mrow><mml:msup><mml:mi>d<\/mml:mi><mml:mn>2<\/mml:mn><\/mml:msup><mml:mi>u<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>d<\/mml:mi><mml:msup><mml:mi>x<\/mml:mi><mml:mn>2<\/mml:mn><\/mml:msup><\/mml:mrow><\/mml:mfrac><mml:mo>+<\/mml:mo><mml:msup><mml:mi>f<\/mml:mi><mml:mo>\u2032<\/mml:mo><\/mml:msup><mml:mrow><mml:mo>(<\/mml:mo><mml:mi>u<\/mml:mi><mml:mo>)<\/mml:mo><\/mml:mrow><mml:mfrac><mml:mrow><mml:mi>d<\/mml:mi><mml:mi>u<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>d<\/mml:mi><mml:mi>x<\/mml:mi><\/mml:mrow><\/mml:mfrac><mml:mo>\u2212<\/mml:mo><mml:mrow><mml:mo>(<\/mml:mo><mml:mrow><mml:mrow><mml:mi>b<\/mml:mi><mml:mo>\/<\/mml:mo><mml:mi>c<\/mml:mi><\/mml:mrow><\/mml:mrow><mml:mo>)<\/mml:mo><\/mml:mrow><mml:mi>u<\/mml:mi><mml:mo>=<\/mml:mo><mml:mn>0<\/mml:mn><\/mml:math>\n where <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>f<\/mml:mi><mml:mrow><mml:mo>(<\/mml:mo><mml:mi>u<\/mml:mi><mml:mo>)<\/mml:mo><\/mml:mrow><mml:mo>=<\/mml:mo><mml:mi>u<\/mml:mi><mml:mrow><mml:mo>(<\/mml:mo><mml:mrow><mml:mn>1<\/mml:mn><mml:mo>\u2212<\/mml:mo><mml:mi>u<\/mml:mi><\/mml:mrow><mml:mo>)<\/mml:mo><\/mml:mrow><mml:mrow><mml:mo>(<\/mml:mo><mml:mrow><mml:mi>u<\/mml:mi><mml:mo>\u2212<\/mml:mo><mml:mi>\u03b1<\/mml:mi><\/mml:mrow><mml:mo>)<\/mml:mo><\/mml:mrow><\/mml:math>\n, <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>0<\/mml:mn><mml:mo>&lt;<\/mml:mo><mml:mi>\u03b1<\/mml:mi><mml:mo>&lt;<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:math>\n. In this paper we\nhave developed a technique to determine those values of the parameters <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>a<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>b<\/mml:mi><\/mml:math>\n and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>c<\/mml:mi><\/mml:math>\n which permit\nnon-constant bounded solutions.<\/jats:p>","DOI":"10.1155\/s1173912699000115","type":"journal-article","created":{"date-parts":[[2007,3,8]],"date-time":"2007-03-08T07:44:28Z","timestamp":1173339868000},"page":"189-193","source":"Crossref","is-referenced-by-count":6,"title":["Classroom Note: Numerical solutions of Nagumo's equation"],"prefix":"10.1080","volume":"3","author":[{"given":"M.","family":"Iqbal","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"301","container-title":["Journal of Applied Mathematics and Decision Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/archive\/1999\/683792.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/archive\/1999\/683792.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T14:22:59Z","timestamp":1723126979000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/ads\/1999\/683792\/abs\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,1,1]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1999,1,1]]}},"alternative-id":["683792"],"URL":"https:\/\/doi.org\/10.1155\/s1173912699000115","relation":{},"ISSN":["1173-9126"],"issn-type":[{"value":"1173-9126","type":"print"}],"subject":[],"published":{"date-parts":[[1999,1,1]]}}}