Chebyshev-Sinc Collocation Schemes for Solving a Class of Convection Diffusion Equations
M. A. Ramadan1, Talaat S. EL-Danaf2, Hanem Galal3
1Mohamed A. Ramadan, Department of Mathematics, Faculty of Science, Menoufia University, Shebein El-Koom, Egypt.
2Talaat S. EL-Danaf, Department of Mathematics, Faculty of Science, Menoufia University, Shebein El-Koom, Egypt.
3Hanem Galal, Department of Mathematics, Faculty of Science, Menoufia University, Shebein El-Koom, Egypt.
Manuscript received on November 02, 2014. | Revised Manuscript received on November 04, 2014. | Manuscript published on November 05, 2014. | PP: 80-87 | Volume-4 Issue-5, November 2014. | Retrieval Number: E1851113513/2014©BEIESP
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© The Authors. Published By: Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: This paper, is concerned with obtaining numerical solutions for a class of convection-diffusion equations (CDEs) with variable coefficients. Our approaches are based on collocation methods. These approaches implementing all four kinds of shifted Chebyshev polynomials in combination with Sinc functions to introduce an approximate solution for CDEs . This approximate solution can be expressed as a finite double summation from the product of Sinc functions and shifted Chebyshev polynomials. The time derivatives for all four kinds of shifted Chebyshev polynomials are expressed here as linear combinations from Chebyshev polynomials themselves. New formulas for the integer derivatives with respect to time t and space x, respectively of the unknown function with two variables is expressed in terms of the product of Sinc functions and shifted Chebyshev polynomials themselves also. Special attention is given to the numerical results obtained by the proposed approaches in order to demonstrate the accuracy and efficiency of the newly proposed approaches.
Keywords: Chebyshev polynomials; Sinc functions – accuracy and efficiency- shifted Chebyshev polynomials.