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Abstract
-The main purpose of this paper is to propose the Chebyshev spectral-collocation method for a class of the weakly singular Volterra integral equations (VIEs) with proportional delay. The proposed method also are applicable to a class of the weakly singular VIEs with proportional delay possessing unsmooth solution. To provide a rigorous error analysis for the proposed method, we prove the the uniqueness and smoothness of the solution. The error analysis shows that the numerical errors decay exponentially in the infinity norm and the Chebyshev weighted Hilbert space norms. Numerical results are presented to confirm the theoretical prediction of the exponential rate of convergence.
Keywords: Chebyshev spectral-collocation method; weakly singular Volterra integral equations; proportional delay; existence and smoothness; error analysis
Received: 2013-8-13
Published Online: 2014-11-25
Published in Print: 2014-12-1
© 2014 by Walter de Gruyter Berlin/Boston