scholarly journals Variable transformations in the numerical solution of second kind Volterra integral equations with continuous and weakly singular kernels; extensions to Fredholm integral equations

2000 ◽  
Vol 115 (1-2) ◽  
pp. 193-211 ◽  
Author(s):  
E.A. Galperin ◽  
E.J. Kansa ◽  
A. Makroglou ◽  
S.A. Nelson
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Volterra Integral Equations ◽  
Fredholm Integral Equations ◽  
Weakly Singular Kernels ◽  
Weakly Singular ◽  
Singular Kernels

scholarly journals A note on orthogonal polynomials

1970 ◽  
Vol 17 (1) ◽  
pp. 83-94 ◽  
Author(s):  
D. Kershaw
Keyword(s):  
Orthogonal Polynomials ◽  
Numerical Solution ◽  
Integral Equations ◽  
Fredholm Integral Equations ◽  
Intermediate Result ◽  
Weakly Singular Kernels ◽  
Quadrature Formulae ◽  
Weakly Singular ◽  
Gauss Type ◽  
Singular Kernels

During an investigation into the existence of Gauss-type quadrature formulae for the numerical solution of Fredholm integral equations with weakly singular kernels an intermediate result was found which is of independent interest.

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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