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Numerical integration of the RLW equation using cubic splines

Published online by Cambridge University Press:  17 February 2009

Dursun Irk ,
İdris Dağ  and
Abdülkadir Doğan
Dursun Irk
Affiliation:
Department of Mathematics, Osmangazi University, Eskişehir, Türkiye; email: ogumath@yahoo.com.
İdris Dağ
Affiliation:
Department of Computer Engineering, Osmangazi University, Eskişehir, Türkiye; e-mail: idag@ogu.edu.tr.
Abdülkadir Doğan
Affiliation:
Department of Mathematics, Niğde University, Niğde, Türkiye.
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Abstract

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A numerical solution of the RLW equation is presented using a cubic spline collocation method. Basic cubic spline relations are outlined and incorporated into the numerical solution procedure. Two test problems are studied to show the robustness of the proposed procedure.

Type
Research Article
Information
The ANZIAM Journal , Volume 47 , Issue 1 , July 2005 , pp. 131 - 142
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Ahlberg, J. H., Nilson, E. N. and Walsh, J. L., The theory of splines and their application (Academic Press, New York, 1967).Google Scholar
[2]Benjamin, T. B., Bona, J. L. and Mahony, J. J., “Model equations for long waves in non-linear dispersive systems”, Phil. Trans. Roy. Soc. London A272 (1972) 47–78Google Scholar
[3]Bhardwaj, D. and Shankar, R., “A computational method for regularised long wave equation”, Comp. Math. Appl. 40 (2000) 1397–1404.CrossRefGoogle Scholar
[4]Bona, J. L., Pritchard, W. G. and Scott, L. R, “An evaluation of a model equation for water waves”, Phil. Trans. Roy. Soc. London A302 (1981) 457–510.Google Scholar
[5]Caldwell, J., “Application of cubic splines to the nonlinear Burgers' equation”, in Numerical Methods for Nonlinear Problems, Vol 3 (ed. Hinton, E. et al. ), (Pineridge Press, Swansea, 1989) 253–261.Google Scholar
[6]Dağ, İ., “Least squares quadratic B-spline finite element method for the regularized long wave equation”, Comp. Methods Appl. Mech. Eng 182 (2000) 205–215.CrossRefGoogle Scholar
[7]Doğan, A., “Numerical solution of regularized long wave equation using Petrov-Galerkin method”, Commum. Numer. Methods Eng. 17 (2001) 485–494.CrossRefGoogle Scholar
[8]Gardner, L. R. T. and Gardner, G. A., “Solitary waves of the regularised long wave equation”, J. Comput. Phys. 91 (1990) 441–459.CrossRefGoogle Scholar
[9]Gardner, L. R. T., Gardner, G. A. and Dağ, İ., “A B-spline finite element method for the regularized long wave equation”, Commum. Numer. Methods Eng. 11 (1995) 59–68.CrossRefGoogle Scholar
[10]Gardner, L. R. T., Gardner, G. A. and Doğan, A., “A least squares finite element scheme for the RLW equation”, Commum. Numer Methods Eng. 12 (1996) 795–804.3.0.CO;2-O>CrossRefGoogle Scholar
[11]Jain, P. C., Shankar, R. and Singh, T. V., “Numerical solution of regularized long-wave equation”, Commum. Numer. Methods Eng. 9 (1993) 579–586.CrossRefGoogle Scholar
[12]Olver, P. J., “Euler operators and conservation laws of the BBM equation”, Math. Proc. Camb. Phil. Soc. 85 (1979) 143–160.CrossRefGoogle Scholar
[13]Peregrine, D. H., “Calculations of the development of an undular bore”, J. Fluid. Mech. 25 (1966) 321–330.CrossRefGoogle Scholar
[14]Rubin, S. G. and Graves, R. A., “Cubic spline approximation for problems in fluid mechanics”, NASA TR R-436, Washington, DC, 1975.Google Scholar
[15]Rubin, S. G. and Khosla, P. K., “Higher-order numerical solutions using cubic splines”, AIAA J. 14 (1976) 851–858.CrossRefGoogle Scholar
[16]Wang, P. and Kahawita, R., “Numerical integration of partial differential equations using cubic splines”, Intern. J. Computer Math. 13 (1983) 271–286.CrossRefGoogle Scholar