AUTHOR=Daba Imiru Takele , Melesse Wondwosen Gebeyaw , Kebede Guta Demisu TITLE=Third-degree B-spline collocation method for singularly perturbed time delay parabolic problem with two parameters JOURNAL=Frontiers in Applied Mathematics and Statistics VOLUME=9 YEAR=2024 URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2023.1260651 DOI=10.3389/fams.2023.1260651 ISSN=2297-4687 ABSTRACT=

This study deals with a fitted third-degree B-spline collocation method for two parametric singularly perturbed parabolic problems with a time lag. The proposed method comprises the Cranck-Nicolson method for time discretization and the third-degree B-spline method spatial variable discretization. Rigorous numerical experimentations were carried out on some test examples. The obtained numerical results depict that the proposed scheme is more accurate than some methods existing in the literature. Parameter convergence analysis of the scheme is carried out and shows the present scheme is (ε−μ)−uniform convergent with the order of convergence ((Δt)2 + ℓ2).