Cubic B-spline Collocation Method for One-Dimensional Heat Equation

Mohamed Hassan Khabir; Rahma Abdullah Farah

doi:doi:10.11648/j.pamj.20170601.17

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Cubic B-spline Collocation Method for One-Dimensional Heat Equation

Mohamed Hassan Khabir, Rahma Abdullah Farah

Published in Pure and Applied Mathematics Journal (Volume 6, Issue 1)

Received: 26 November 2016 Accepted: 16 January 2017 Published: 4 March 2017

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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.

Published in	Pure and Applied Mathematics Journal (Volume 6, Issue 1)
DOI	10.11648/j.pamj.20170601.17
Page(s)	51-58
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Cubic B-spline, Collocation Method, Heat Equation, Linear Partial Differential Equation

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.

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APA Style

Mohamed Hassan Khabir, Rahma Abdullah Farah. (2017). Cubic B-spline Collocation Method for One-Dimensional Heat Equation. Pure and Applied Mathematics Journal, 6(1), 51-58. https://doi.org/10.11648/j.pamj.20170601.17

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ACS Style

Mohamed Hassan Khabir; Rahma Abdullah Farah. Cubic B-spline Collocation Method for One-Dimensional Heat Equation. Pure Appl. Math. J. 2017, 6(1), 51-58. doi: 10.11648/j.pamj.20170601.17

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AMA Style

Mohamed Hassan Khabir, Rahma Abdullah Farah. Cubic B-spline Collocation Method for One-Dimensional Heat Equation. Pure Appl Math J. 2017;6(1):51-58. doi: 10.11648/j.pamj.20170601.17

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@article{10.11648/j.pamj.20170601.17,
  author = {Mohamed Hassan Khabir and Rahma Abdullah Farah},
  title = {Cubic B-spline Collocation Method for One-Dimensional Heat Equation},
  journal = {Pure and Applied Mathematics Journal},
  volume = {6},
  number = {1},
  pages = {51-58},
  doi = {10.11648/j.pamj.20170601.17},
  url = {https://doi.org/10.11648/j.pamj.20170601.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20170601.17},
  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.},
 year = {2017}
}

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TY  - JOUR
T1  - Cubic B-spline Collocation Method for One-Dimensional Heat Equation
AU  - Mohamed Hassan Khabir
AU  - Rahma Abdullah Farah
Y1  - 2017/03/04
PY  - 2017
N1  - https://doi.org/10.11648/j.pamj.20170601.17
DO  - 10.11648/j.pamj.20170601.17
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
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PB  - Science Publishing Group
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AB  - 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.
VL  - 6
IS  - 1
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Author Information

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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Plain Text BibTeX RIS

APA Style

Mohamed Hassan Khabir, Rahma Abdullah Farah. (2017). Cubic B-spline Collocation Method for One-Dimensional Heat Equation. Pure and Applied Mathematics Journal, 6(1), 51-58. https://doi.org/10.11648/j.pamj.20170601.17

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ACS Style

Mohamed Hassan Khabir; Rahma Abdullah Farah. Cubic B-spline Collocation Method for One-Dimensional Heat Equation. Pure Appl. Math. J. 2017, 6(1), 51-58. doi: 10.11648/j.pamj.20170601.17

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AMA Style

Mohamed Hassan Khabir, Rahma Abdullah Farah. Cubic B-spline Collocation Method for One-Dimensional Heat Equation. Pure Appl Math J. 2017;6(1):51-58. doi: 10.11648/j.pamj.20170601.17

Copy | Download

@article{10.11648/j.pamj.20170601.17,
  author = {Mohamed Hassan Khabir and Rahma Abdullah Farah},
  title = {Cubic B-spline Collocation Method for One-Dimensional Heat Equation},
  journal = {Pure and Applied Mathematics Journal},
  volume = {6},
  number = {1},
  pages = {51-58},
  doi = {10.11648/j.pamj.20170601.17},
  url = {https://doi.org/10.11648/j.pamj.20170601.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20170601.17},
  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.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Cubic B-spline Collocation Method for One-Dimensional Heat Equation
AU  - Mohamed Hassan Khabir
AU  - Rahma Abdullah Farah
Y1  - 2017/03/04
PY  - 2017
N1  - https://doi.org/10.11648/j.pamj.20170601.17
DO  - 10.11648/j.pamj.20170601.17
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 51
EP  - 58
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20170601.17
AB  - 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.
VL  - 6
IS  - 1
ER  -

Copy | Download