{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,26]],"date-time":"2025-12-26T00:04:15Z","timestamp":1766707455713,"version":"3.48.0"},"reference-count":30,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,12,25]],"date-time":"2025-12-25T00:00:00Z","timestamp":1766620800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Graduate Studies and Scientific Research at Qassim University","award":["QU-APC-2025"],"award-info":[{"award-number":["QU-APC-2025"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This work focuses on solving the singularly perturbed generalized Hodgkin-Huxley (HH) problem. The HH equation is numerically solved by a collocation approach using third-degree splines. The forward difference technique is utilized for time discretization, while \u03b8-weighted schemes are employed for space discretization. Solving non-linear models using discretization and quasi-linearization results in a set of linear algebraic equations, which are solved using matrices. Furthermore, Von Neumann\u2019s (VN) stability and Spectral Radius (S.R) reveal that the suggested technique is unconditionally stable. To assess the performance and accuracy of this method, absolute error (AE), L2, and L\u221e norms are offered. The results align with the literature. Simulation results show that the proposed strategy produces accurate results.<\/jats:p>","DOI":"10.3390\/axioms15010012","type":"journal-article","created":{"date-parts":[[2025,12,25]],"date-time":"2025-12-25T23:52:27Z","timestamp":1766706747000},"page":"12","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Computational Study of Singularly Perturbed Neurodynamical Models via Cubic B-Spline"],"prefix":"10.3390","volume":"15","author":[{"given":"Alina","family":"Yousafzai","sequence":"first","affiliation":[{"name":"Faculty of Engineering Sciences, GIK Institute, Topi 23640, KP, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tanveer","family":"Akbar","sequence":"additional","affiliation":[{"name":"Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Peshawar 25000, KP, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8309-6121","authenticated-orcid":false,"given":"Khidir Shaib","family":"Mohamed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science Qassim University, Buraydah 51452, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alawia","family":"Adam","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science Qassim University, Buraydah 51452, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mona A.","family":"Mohamed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science Qassim University, Buraydah 51452, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4681-9885","authenticated-orcid":false,"given":"Waseem Ahmad","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Prince Mohammad Bin Fahd University, Al Khobar 31952, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5103-6092","authenticated-orcid":false,"given":"Azhar","family":"Iqbal","sequence":"additional","affiliation":[{"name":"Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, Al Khobar 31952, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,12,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4670","DOI":"10.1016\/j.jde.2008.12.025","article-title":"Robust Exponential Attractors for Singularly Perturbed Hodgkin\u2013Huxley Equations","volume":"246","author":"Cavaterra","year":"2009","journal-title":"J. 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