A Chebyshev Polynomial Approach for High-Order Linear Fredholm-Volterra Integro-Differential Equations

Gamze Yuksel; Mehmet Sezer; Mustafa Gulsu

A Chebyshev Polynomial Approach for High-Order Linear Fredholm-Volterra Integro-Differential Equations

Year 2012, Volume: 25 Issue: 2, 393 - 401, 16.04.2012

Gamze Yuksel , Mehmet Sezer Mustafa Gulsu

Abstract

The purpose of this study is to present a method for solving high order linear Fredholm-Volterra integro-differential equations in terms of Chebyshev polynomials under the mixed conditions. The method is based on the approximation by the truncated Chebyshev series. The higher order linear Fredholm-Volterra integro-differential equations and the conditions are transformed into the matrix equations, which corresponds to a system of linear algebraic equations with the unknown Chebyshev coefficients. Combining these matrix equations and then solving the system yields the Chebyshev coefficients of the solution function. Finally, the effectiveness of the method is illustrated in several numerical experiments and error analysis is performed.

Keywords: Chebyshev polynomials, Fredholm-Volterra integral equations, Polynomial approximations

Keywords

Chebyshev polynomials, Fredholm-Volterra integral equations, Polynomial approximations

Equations

Year 2012, Volume: 25 Issue: 2, 393 - 401, 16.04.2012

Gamze Yuksel , Mehmet Sezer Mustafa Gulsu

Abstract

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Details

Journal Section	Mathematics
Authors	Gamze Yuksel Mehmet Sezer This is me Mustafa Gulsu This is me
Publication Date	April 16, 2012
Published in Issue	Year 2012 Volume: 25 Issue: 2

Cite

APA	Yuksel, G., Sezer, M., & Gulsu, M. (2012). A Chebyshev Polynomial Approach for High-Order Linear Fredholm-Volterra Integro-Differential Equations. Gazi University Journal of Science, 25(2), 393-401.
AMA	Yuksel G, Sezer M, Gulsu M. A Chebyshev Polynomial Approach for High-Order Linear Fredholm-Volterra Integro-Differential Equations. Gazi University Journal of Science. April 2012;25(2):393-401.
Chicago	Yuksel, Gamze, Mehmet Sezer, and Mustafa Gulsu. “A Chebyshev Polynomial Approach for High-Order Linear Fredholm-Volterra Integro-Differential Equations”. Gazi University Journal of Science 25, no. 2 (April 2012): 393-401.
EndNote	Yuksel G, Sezer M, Gulsu M (April 1, 2012) A Chebyshev Polynomial Approach for High-Order Linear Fredholm-Volterra Integro-Differential Equations. Gazi University Journal of Science 25 2 393–401.
IEEE	G. Yuksel, M. Sezer, and M. Gulsu, “A Chebyshev Polynomial Approach for High-Order Linear Fredholm-Volterra Integro-Differential Equations”, Gazi University Journal of Science, vol. 25, no. 2, pp. 393–401, 2012.
ISNAD	Yuksel, Gamze et al. “A Chebyshev Polynomial Approach for High-Order Linear Fredholm-Volterra Integro-Differential Equations”. Gazi University Journal of Science 25/2 (April 2012), 393-401.
JAMA	Yuksel G, Sezer M, Gulsu M. A Chebyshev Polynomial Approach for High-Order Linear Fredholm-Volterra Integro-Differential Equations. Gazi University Journal of Science. 2012;25:393–401.
MLA	Yuksel, Gamze et al. “A Chebyshev Polynomial Approach for High-Order Linear Fredholm-Volterra Integro-Differential Equations”. Gazi University Journal of Science, vol. 25, no. 2, 2012, pp. 393-01.
Vancouver	Yuksel G, Sezer M, Gulsu M. A Chebyshev Polynomial Approach for High-Order Linear Fredholm-Volterra Integro-Differential Equations. Gazi University Journal of Science. 2012;25(2):393-401.