scholarly journals A spectral technique for solving two-dimensional fractional integral equations with weakly singular kernel

2017 ◽  
Vol 5 (46) ◽  
Author(s):  
Ali H. Bhrawy
Keyword(s):  
Integral Equations ◽  
Fractional Integral ◽  
Singular Kernel ◽  
Two Dimensional ◽  
Weakly Singular Kernel ◽  
Spectral Technique ◽  
Weakly Singular

Convergence Analysis of the Spectral Method for Second-Kind Volterra Integral Equations with a Weakly Singular Kernel

2012 ◽  
Vol 263-266 ◽  
pp. 3313-3316
Author(s):  
Yiao Yong Zhang ◽  
Hua Feng Wu
Keyword(s):  
Integral Equations ◽  
Source Function ◽  
Volterra Integral Equations ◽  
Singular Kernel ◽  
Weakly Singular Kernel ◽  
Weakly Singular ◽  
L2 Norm ◽  
Spectral Galerkin Method ◽  
Rigorous Error ◽  
Theoretical Results

The Legendre spectral Galerkin method for Volterra integral equations of the second kind with a weakly singular kernel is proposed in this paper. 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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