Share This Article:

On Approximate Solutions of Second-Order Linear Partial Differential Equations

Full-Text HTML XML Download Download as PDF (Size:162KB) PP. 1001-1007
DOI: 10.4236/am.2012.39148    4,211 Downloads   6,705 Views   Citations
Author(s)    Leave a comment

ABSTRACT

In this paper, a Chebyshev polynomial approximation for the solution of second-order partial differential equations with two variables and variable coefficients is given. Also, Chebyshev matrix is introduced. This method is based on taking the truncated Chebyshev expansions of the functions in the partial differential equations. Hence, the result matrix equation can be solved and approximate value of the unknown Chebyshev coefficients can be found.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Y. Hanna, "On Approximate Solutions of Second-Order Linear Partial Differential Equations," Applied Mathematics, Vol. 3 No. 9, 2012, pp. 1001-1007. doi: 10.4236/am.2012.39148.

References

[1] X. F. Yang, Y. X. Liu and S. Bai, “A Numerical Solution of Second-Order Linear Partial Differential Equations by Differential Transform,” Journal of Applied Mathematics and Computing, Vol. 173, No. 2, 2006, pp. 792-802. doi:10.1016/j.amc.2005.04.015
[2] Luhong Ye and Zhiting Xu, “Oscillation Criteria for Second Order Quasilinear Neutral Delay Differential Equations,” Journal of Applied Mathematics and Computing, Vol. 207, No. 2, 2009, pp. 388-396. doi:10.1016/j.amc.2008.10.051
[3] M. Sezer and M. Kaynak, “Chebyshev Polynomial Solutions of Linear Differential Equations,” International Journal of Mathematical Education in Science & Technology, Vol. 27, No. 4, 1996, pp. 607-618. doi:10.1080/0020739960270414
[4] N. K. Basu, “On Double Chebyshev Series Approximation,” SIAM Journal on Numerical Analysis, Vol. 10, No. 3, 1973, pp. 496-505. doi:10.1137/0710045
[5] F. Cases, “Solution of Linear Partial Differential Equations by Lie Algebraic Methods,” Journal of Computational and Applied Mathematics, Vol. 76, No. 1-2, 1996, pp. 159-170.
[6] H. Koroglu, “Chebyshev Series Solution of Linear Fredholm Integrodifferential Equations,” International Journal of Mathematical Education in Science & Technology, Vol. 29, No. 4, 1998, pp. 489-500. doi:10.1080/0020739980290403
[7] V. S. Vladimirov, “A Collection of Problems on the Equations of Mathematical Physics,” Mir Publishers, Moscow, 1986, pp. 139-149.

  
comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.