Cubic B-spline Collocation Method for One-Dimensional Heat Equation
Pure and Applied Mathematics Journal
Volume 6, Issue 1, February 2017, Pages: 51-58
Received: Nov. 26, 2016; Accepted: Jan. 16, 2017; Published: Mar. 4, 2017
Views 2171      Downloads 191
Authors
Mohamed Hassan Khabir, Department of Mathematics, Faculty of Science, Sudan University of Science & Technology, Khartoum, Sudan
Rahma Abdullah Farah, Department of Mathematics, Faculty of Science & Technology, Omdurman Islamic University, Khartoum, Sudan
Article Tools
Follow on us
Abstract
In this paper we discuss cubic B-spline collocation method. We have given the derivation of the B-spline method in general. We have applied the method for solving one-dimensional heat equation and the numerical result have been compared with the exact solution.
Keywords
Cubic B-spline, Collocation Method, Heat Equation, Linear Partial Differential Equation
To cite this article
Mohamed Hassan Khabir, Rahma Abdullah Farah, Cubic B-spline Collocation Method for One-Dimensional Heat Equation, Pure and Applied Mathematics Journal. Vol. 6, No. 1, 2017, pp. 51-58. doi: 10.11648/j.pamj.20170601.17
Copyright
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
References
[1]
H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids, Oxford University Pres., 1959.
[2]
I. Dag, B. Saka, D. Irk, Application Cubic B-splines for Numerical Solution of the RLW Equation, Appl. Maths. and Comp., 159 (2004) 373–389.
[3]
D. V. Widder, The Heat Equation, Academic Press, 1976.
[4]
J. R. Cannon, The One-Dimensional Heat Equation, Cambridge University Pres., 1984.
[5]
en.wikipedia.org/wiki/Heat_equation.
[6]
JBJ Fourier, Theorie analytique dela Chaleur, Didot Paris: 499-508 (1822).
[7]
J. M. Ahlberg, E. N. Nilson, J. L. Walsh, The Theory of splines and Their Applications, Academic Press, New York, 1967.
[8]
M. K. Kadalbajoo and V. K. Aggarwal, Fitted mesh B-spline collocation method for solving self-adjoint singularly perturbed boundary value problems, Applied Mathematics and Computation 161 (2005), 973–987.
[9]
G. Micula, Handbook of Splines, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1999.
[10]
L. L. Schumaker, Spline Functions: Basic Theory, Krieger Publishing Company, Florida, 1981.
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186