Abstract

This study presents a numerical method for the solution of one type of PDEs equation. In this study, apply the pseudo-spectral successive integration method to approximate the solution of the one-dimensional parabolic equation. This method is based on El-Gendi pseudo-spectral method. Also the Finite Difference Method (FDM) is used as a minor method. The present numerical results are in satisfactory agreement with exact solution.

Keywords:

El-Gendi method, Gauss-Lobatto points, pseudo-spectral successive integration, parabolic equation,

References

1. Clenshaw, C.W. and A.R. Curtis, 1960. A method for numerical integration on an automatic computer. Numer. Math., 2: 197-149.
   CrossRef    
2. Dehghan, M. and M. Tatari, 2006. Determination of a control parameter in a one-dimensional parabolic equation using the method of radial basis functions. Math. Comput. Model., 44: 1160-1168.
   CrossRef    
3. Delves, L.M. and J.L. Mohamed, 1985. Computational Methods for Integral Equations. Cambridge University Press, New York.
   CrossRef    
4. Elbarbary, E.M.E., 2007. Pseudospectral integration matrix and boundary value problems. Int. J. Comput. Math., 84: 1851-1861.
   CrossRef    
5. El-Gendi, S.E., 1969. Chebyshev solution of differential, integral and integro-differential equations. Comput. J., 12: 282-287.
   CrossRef    
6. El-Gendi, S.E., 1975. Chebyshev solution of parabolic partial differential equations. J. I. Math. Appl., 16: 283-289.
   CrossRef    
7. El-Gendi, S.E., H. Nasr and H.M. El-Hawary, 1992. Numerical solution of poisson's equation by expansion in Chebyshev polynomials. Bull. Calcutta Math. Soc., 84: 443-449.
   
8. Elgindy, K.T., 2009. Generation of higher order pseudo-spectral integration matrices. Appl. Math. Comput., 209: 153-161.
   CrossRef    
9. Hatziavramidis, D. and H.C. Ku, 1985. An integral Chebyshev expansion method for boundary value problems of O.D.E. type. Comput. Math. Appl., 11: 581-586.
   CrossRef    
10. Jeffreys, H. and B.S. Jeffreys, 1956. Methods of Mathematical Physics. Cambridge University Press, New York.
    
11. Khalifa, A.K., E.M.E. Elbarbary and M.A. Abd-Elrazek, 2003. Chebyshev expansion method for solving second and fourth order elliptic equations. Appl. Math. Comput., 135: 307-318.
    CrossRef    
12. Nasr, H. and H.M. El-Hawary, 1991.Chebyshev method for the solution of boundary value problems. Int. J. Comput. Math., 40: 251-258.
    CrossRef    
13. Nasr, H., I.A. Hassanien and H.M. El-Hawary, 1990. Chebyshev solution laminar boundary layer flow. Int. J. Comput. Math., 33: 127-132.
    CrossRef    
14. Strikverda, J.C., 2004. Finite Difference Schemes and Partial Differential Equations. Wadsworth, Pacif Grove, California.
    CrossRef    

Competing interests

The authors have no competing interests.

Open Access Policy

This article is 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, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Copyright

The authors have no competing interests.