scholarly journals Smoothing transformation and piecewise polynomial projection methods for weakly singular Fredholm integral equations

2006 ◽  
Vol 5 (2) ◽  
pp. 395-413 ◽  
Author(s):  
A. Pedas ◽  
◽  
G. Vainikko
Keyword(s):  
Integral Equations ◽  
Projection Methods ◽  
Fredholm Integral Equations ◽  
Piecewise Polynomial ◽  
Weakly Singular ◽  
Smoothing Transformation

Numerical Algorithms of Optimal Complexity for Weakly Singular Volterra Integral Equations

2006 ◽  
Vol 6 (4) ◽  
pp. 436-442 ◽  
Author(s):  
A.N. Tynda
Keyword(s):  
Numerical Methods ◽  
Integral Equations ◽  
Numerical Algorithms ◽  
Volterra Integral Equations ◽  
Volterra Equations ◽  
Fredholm Integral Equations ◽  
Optimal Complexity ◽  
Weakly Singular ◽  
Different Types ◽  
Singular Kernels

AbstractIn this paper we construct complexity order optimal numerical methods for Volterra integral equations with different types of weakly singular kernels. We show that for Volterra equations (in contrast to Fredholm integral equations) using the ”block-by-block” technique it is not necessary to employ the additional iterations to construct complexity optimal methods.

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