Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 67, Issue 1, Pages 43-64Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-015-0069-5
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Funding
- National NSF of China [11201077, 11471274, 11421110001, 91130002]
- NSF of Fujian Province [2012J01007]
- Fuzhou University [0460022456]
- Hong Kong Research Grant Council GIF Grants
- Hong Kong Baptist University FRG Grants
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In this paper we present and analyze Chebyshev and Legendre pseudo-spectral methods for the second kind Volterra integral equations with weakly singular kernel (x - s)(-mu), 0 < mu < 1. The proposed methods are based on the Gauss-type quadrature formula for approximating the integral operators involved in the equations. The present work is an extension of the earlier proposed spectral Jacobi-Galerkin method for the second kind Volterra integral equations with regular kernels (Xie et al. in J Sci Comput 53(2):414-434, [21]). Adetailed convergence analysis is carried out, and several error estimates in L-infinity and L-omega(2) norms are obtained. Numerical examples are considered to verify the theoretical predictions.
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