Zhang Xiao-Yong
Shanghai Maritime University, China
Wu Huafeng
Merchant Marine College, Shanghai Maritime University, China
ABSTRACT
The Jacobi pseudo-spectral Galerkin method for the weakly singular Volterra integral equations of the second kind with smooth solutions is proposed in this study. We provide a rigorous error analysis for the proposed method which indicates that the numerical errors (in the L2-norm and the L∞-norm ) will decay exponentially provided that the source function is sufficiently smooth. Numerical examples are given to illustrate the theoretical results.
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How to cite this article
Zhang Xiao-Yong and Wu Huafeng, 2013. On Pseudo-spectral Method for Second-kind Weakly Singularvolterra Integral Equations with Smooth Solutions. Information Technology Journal, 12: 7401-7408.
DOI: 10.3923/itj.2013.7401.7408
URL: https://scialert.net/abstract/?doi=itj.2013.7401.7408
DOI: 10.3923/itj.2013.7401.7408
URL: https://scialert.net/abstract/?doi=itj.2013.7401.7408
REFERENCES
- Chen, Y.P. and T. Tang, 2009. Spectral methods for weakly singular Volterra integral equations with smooth solutions. J. Computat. Applied Math., 233: 938-950.
CrossRefDirect Link - Chen, Y.P. and T. Tang, 2010. Convergence analysis of the Jacobi Spectral-Collocation methods for Volterra integral equations with a weakly singular kernel. Math. Comput., 79: 147-167.
Direct Link - Federson, M., R. Bianconi and L. Barbanti, 2003. Linear Volterra integral equations as the limit of discrete systems. Cadernos Matematica, 4: 331-352.
Direct Link - Gogatishvill, A. and J. Lang, 1999. The generalized hardy operator with kernel and variable integral limits in banach function spaces. J. Inequalities Appl., Vol. 4.
CrossRef - Jiang, Y.J., 2009. On spectral methods for Volterra-type Integro-differential equations. J. Comput, Appl. Math., 230: 333-340.
CrossRefDirect Link - Ragozin, D.L., 1970. Polynomial approximation on compact manifolds and homogeneous spaces. Trans. Am. Math. Soc., 150: 41-53.
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