Journal of Applied Mathematics
Volume 2012 (2012), Article ID 458701, 8 pages
Research Article

Cubic B-Spline Collocation Method for One-Dimensional Heat and Advection-Diffusion Equations

Pusat Pengajian Sains Matematik, Universiti Sains Malaysia, 11800 Pulau Pinang, Malaysia

Received 12 January 2012; Accepted 9 March 2012

Academic Editor: Ram N. Mohapatra

Copyright © 2012 Joan Goh et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Numerical solutions of one-dimensional heat and advection-diffusion equations are obtained by collocation method based on cubic B-spline. Usual finite difference scheme is used for time and space integrations. Cubic B-spline is applied as interpolation function. The stability analysis of the scheme is examined by the Von Neumann approach. The efficiency of the method is illustrated by some test problems. The numerical results are found to be in good agreement with the exact solution.