An hp-Version Chebyshev Spectral Collocation Method for Nonlinear Volterra Integro-Differential Equations with Weakly Singular Kernels

2019 ◽  
Vol 12 (3) ◽  
pp. 969-994
Author(s):  
Hongli Jia
Keyword(s):  
Differential Equations ◽  
Collocation Method ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Weakly Singular Kernels ◽  
Weakly Singular ◽  
Chebyshev Spectral Collocation ◽  
Singular Kernels ◽  
Chebyshev Spectral Collocation Method

Chebyshev spectral-collocation method for a class of weakly singular Volterra integral equations with proportional delay

2014 ◽  
Vol 22 (4) ◽  
Author(s):  
Z. Gu ◽  
Y. Chen
Keyword(s):  
Error Analysis ◽  
Integral Equations ◽  
Collocation Method ◽  
Volterra Integral Equations ◽  
Spectral Collocation Method ◽  
Proportional Delay ◽  
Spectral Collocation ◽  
Weakly Singular ◽  
Chebyshev Spectral Collocation ◽  
Chebyshev Spectral Collocation Method

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.

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