scholarly journals TWO-GRID ITERATION METHOD FOR WEAKLY SINGULAR INTEGRAL EQUATIONS

2000 ◽  
Vol 5 (1) ◽  
pp. 76-85
Author(s):  
K. Hakk
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Iteration Method ◽  
Singular Integral Equations ◽  
Piecewise Polynomial ◽  
Weakly Singular ◽  
Weakly Singular Integral Equations ◽  
Piecewise Polynomial Collocation Method ◽  
Large Linear Systems ◽  
Polynomial Collocation

For the solution of weakly singular integral equations by the piecewise polynomial collocation method it is necessary to solve large linear systems. In the present paper a two‐grid iteration method for solving such systems is constructed and the convergence of this method is investigated.

scholarly journals ON THE STABILITY OF PIECEWISE POLYNOMIAL COLLOCATION METHODS FOR SOLVING WEAKLY SINGULAR INTEGRAL EQUATIONS OF THE SECOND KIND

2008 ◽  
Vol 13 (1) ◽  
pp. 29-36 ◽  
Author(s):  
R. Kangro ◽  
I. Kangro
Keyword(s):  
Integral Equations ◽  
Singular Integral Equations ◽  
Collocation Methods ◽  
Piecewise Polynomial ◽  
Nonuniform Grids ◽  
Weakly Singular ◽  
Weakly Singular Integral Equations ◽  
The Stability ◽  
Implementation Problems ◽  
Polynomial Collocation

Piecewise polynomial collocation methods on special nonuniform grids are efficient methods for solving weakly singular Fredholm and Volterra integral equations but there is a widespread belief that those methods are numerically unstable in the case of large values of the nonuniformity parameter r. We show that this method by itself is stable and discuss some implementation problems that may lead to unstable behavior of numerical results.

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