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
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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
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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.
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.
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.
H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids, Oxford University Pres., 1959.
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.
D. V. Widder, The Heat Equation, Academic Press, 1976.
J. R. Cannon, The One-Dimensional Heat Equation, Cambridge University Pres., 1984.
JBJ Fourier, Theorie analytique dela Chaleur, Didot Paris: 499-508 (1822).
J. M. Ahlberg, E. N. Nilson, J. L. Walsh, The Theory of splines and Their Applications, Academic Press, New York, 1967.
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.
G. Micula, Handbook of Splines, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1999.
L. L. Schumaker, Spline Functions: Basic Theory, Krieger Publishing Company, Florida, 1981.