Volterra Integral Equations with Vanishing Delay
Applied and Computational Mathematics
Volume 4, Issue 3, June 2015, Pages: 152-161
Received: Mar. 29, 2015;
Accepted: May 6, 2015;
Published: May 27, 2015
Views 4024 Downloads 173
Xiaoxuan Li, Department of Mathematics and Statistics, Hanshan Normal University, Chaozhou, China
Weishan Zheng, Department of Mathematics and Statistics, Hanshan Normal University, Chaozhou, China
Jiena Wu, Department of Mathematics and Statistics, Hanshan Normal University, Chaozhou, China
Follow on us
In this article, we use a Chebyshev spectral-collocation method to solve the Volterra integral equations with vanishing delay. Then a rigorous error analysis provided by the proposed method shows that the numerical error decay exponentially in the infinity norm and in the Chebyshev weighted Hilbert space norm. Numerical results are presented, which confirm the theoretical predicition of the exponential rate of convergence.
Chebyshev Spectral-Collocation Method, Volterra Integral Equations, Vanishing Delay, Error Estimate, Convergence Analysis
To cite this article
Volterra Integral Equations with Vanishing Delay, Applied and Computational Mathematics.
Vol. 4, No. 3,
2015, pp. 152-161.
T. Tang, X. Xu, J. Cheng, On spectral methods for Volterra type integral equations and the convergence analysis, J. Comput. Math. 26 (2008) 825-837.
Y. Chen, and T. Tang, Convergence analysis of the Jacobi spectral-collocation methods for Volterra integral equation with a weakly singular kernel, Math. Comput. 79(2010), pp. 147–167.
Z. Wan, Y. Chen, and Y. Huang, Legendre spectral Galerkin method for second-kind Volterraintegral equations, Front. Math. China, 4(2009), pp. 181–193.
Z. Xie, X. Li and T. Tang, Convergence Analysis of Spectral Galerkin Methods for Volterra Type Integral Equations, J. Sci. Comput, 2012.
Z. Gu and Y. Chen, Chebyshev spectral collocation method for Volterra integral equations [D•Master's Thesis], Contemporary Mathematics, Volume 586, 2013, pp. 163-170.
C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral method fundamentalsin single domains, Spring-Verlag, 2006.
J. Shen, and T. Tang, Spectral and high-order methods with applications, Science Press, Beijing, 2006.
D. Henry, Geometric theory of semilinear parabolic equations, Springer-Verlag, 1989.
A. Kufner, and L. E. Persson, Weighted inequality of Hardy’s Type, World scientific, NewYork, 2003.
P. Nevai, Mean convergence of Lagrange interpolation, III, Trans. Amer. Math. Soc., 282(1984), pp. 669–698.