Open AccessNumerical Method Using Cubic B-Spline for a Strongly Coupled Reaction-Diffusion System
Author(s) -
Muhammad Abbas,
Ahmad Abd. Majid,
Ahmad Izani Md. Ismail,
Abdur Rashid
Publication year - 2014
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0083265
Subject(s) - discretization , spline interpolation , mathematics , reaction–diffusion system , monotone cubic interpolation , thin plate spline , mathematical analysis , collocation method , interpolation (computer graphics) , boundary value problem , b spline , neumann boundary condition , finite difference method , finite difference , numerical analysis , linear interpolation , physics , polynomial interpolation , differential equation , ordinary differential equation , polynomial , motion (physics) , statistics , classical mechanics , bilinear interpolation
In this paper, a numerical method for the solution of a strongly coupled reaction-diffusion system, with suitable initial and Neumann boundary conditions, by using cubic B-spline collocation scheme on a uniform grid is presented. The scheme is based on the usual finite difference scheme to discretize the time derivative while cubic B-spline is used as an interpolation function in the space dimension. The scheme is shown to be unconditionally stable using the von Neumann method. The accuracy of the proposed scheme is demonstrated by applying it on a test problem. The performance of this scheme is shown by computinganderror norms for different time levels. The numerical results are found to be in good agreement with known exact solutions.
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