Chelyshkov collocation approach for solving linear weakly singular Volterra integral equations

2018 ◽  
Vol 60 (1-2) ◽  
pp. 201-222 ◽  
Author(s):  
Y. Talaei
Keyword(s):  
Integral Equations ◽  
Volterra Integral Equations ◽  
Weakly Singular ◽  
Collocation Approach

scholarly journals Superconvergence of interpolated collocation solutions for weakly singular Volterra integral equations of the second kind

2021 ◽  
Vol 40 (3) ◽  
Author(s):  
Qiumei Huang ◽  
Min Wang
Keyword(s):  
Integral Equations ◽  
Numerical Experiments ◽  
Volterra Integral Equations ◽  
Least Square ◽  
Convergence Order ◽  
Collocation Points ◽  
Weakly Singular ◽  
Interpolation Postprocessing ◽  
Collocation Solution

AbstractIn this paper, we discuss the superconvergence of the “interpolated” collocation solutions for weakly singular Volterra integral equations of the second kind. Based on the collocation solution $$u_h$$ u h , two different interpolation postprocessing approximations of higher accuracy: $$I_{2h}^{2m-1}u_h$$ I 2 h 2 m - 1 u h based on the collocation points and $$I_{2h}^{m}u_h$$ I 2 h m u h based on the least square scheme are constructed, whose convergence order are the same as that of the iterated collocation solution. Such interpolation postprocessing methods are much simpler in computation. We further apply this interpolation postprocessing technique to hybrid collocation solutions and similar results are obtained. Numerical experiments are shown to demonstrate the efficiency of the interpolation postprocessing methods.

scholarly journals A linear approximation for solutions of Abel–Volterra integral equations

2020 ◽  
Vol 14 (2) ◽  
pp. 596-604
Author(s):  
Mostefa Nadir
Keyword(s):  
Integral Equations ◽  
Linear Approximation ◽  
Singular Integral ◽  
Volterra Integral Equations ◽  
New Technique ◽  
Numerical Examples ◽  
Weakly Singular

Abstract In this work, we present a modified linear approximation for solving the first and the second kind Abel–Volterra integral equations. This approximation was used by the author to approximate a weakly singular integral on the curve. Noting that this new technique gives a good approximation of these solutions compared with several methods in several numerical examples.

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