Smoothing transformation and cubic spline collocation for weakly singular Fredholm integral equations with boundary singularities

2012 ◽  
Author(s):  
Arvet Pedas ◽  
Mikk Vikerpuur
Keyword(s):  
Integral Equations ◽  
Cubic Spline ◽  
Fredholm Integral Equations ◽  
Spline Collocation ◽  
Weakly Singular ◽  
Cubic Spline Collocation ◽  
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.

Modified nodal cubic spline collocation for biharmonic equations

2007 ◽  
Vol 43 (4) ◽  
pp. 331-353 ◽  
Author(s):  
Abeer Ali Abushama ◽  
Bernard Bialecki
Keyword(s):  
Cubic Spline ◽  
Spline Collocation ◽  
Biharmonic Equations ◽  
Cubic Spline Collocation
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