Abstract
Abstract
This work reports a collocation algorithm for the numerical solution of a Volterra–Fredholm integral equation (V-FIE), using shifted Chebyshev collocation (SCC) method. Some properties of the shifted Chebyshev polynomials are presented. These properties together with the shifted Gauss–Chebyshev nodes were then used to reduce the Volterra–Fredholm integral equation to the solution of a matrix equation. Nextly, the error analysis of the proposed method is presented. We compared the results of this algorithm with others and showed the accuracy and potential applicability of the given method.
Publisher
Springer Science and Business Media LLC
Reference28 articles.
1. Abd-Elhameed, W.M.; Youssri, Y.H.: Numerical solutions for Volterra–Fredholm–Hammerstein integral equations via second kind Chebyshev quadrature collocation algorithm. Adv. Math. Sci. Appl. 24, 129–141 (2014)
2. Abd-Elhameed, W.M.; Youssri, Y.H.: Fifth-kind orthonormal Chebyshev polynomial solutions for fractional differential equations. Comp. Appl. Math. 37(3), 2897–2921 (2018)
3. Abd-Elhameed, W.M.; Doha, E.H.; Youssri, Y.H.; Bassuony, M.A.: New Tchebyshev-Galerkin operational matrix method for solving linear and nonlinear hyperbolic telegraph type equations. Numer. Methods Partial Diff. Equ. 32(6), 1553–1571 (2016)
4. Brunner, H.: On the numerical solution of Volterra–Fredholm integral equation by collocation methods. SIAM J. Numer. Anal. 27(4), 87–96 (1990)
5. Cardone, A.; Messina, E.; Vecchio, A.: An adaptive method for Volterra–Fredholm integral equations on the half line. J. Comput. Appl. Math. 228, 538–547 (2009)
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