Two-Grid Solution of Symm's Integral Equation

1996 ◽  
Vol 177 (1) ◽  
pp. 265-279 ◽  
Author(s):  
J. Saranen ◽  
G. Vainikko
Keyword(s):  
Integral Equation ◽  
Grid Solution ◽  
Symm’S Integral Equation

scholarly journals A discrete method for the logarithmic-kernel integral equation on an open arc

1993 ◽  
Vol 34 (4) ◽  
pp. 401-418 ◽  
Author(s):  
S. Prössdorf ◽  
J. Saranen ◽  
I. H. Sloan
Keyword(s):  
Integral Equation ◽  
Stability And Convergence ◽  
Quadrature Method ◽  
Closed Curves ◽  
Discrete Method ◽  
Logarithmic Kernel ◽  
Quadrature Scheme ◽  
The Family ◽  
The Stability ◽  
Symm’S Integral Equation

AbstractHere we discuss the stability and convergence of a quadrature method for Symm's integral equation on an open smooth arc. The method is an adaptation of an approach considered by Sloan and Burn for closed curves. Before applying the quadrature scheme, we use a cosine substitution to remove the endpoint singularity of the solution. The family of methods includes schemes with any order O(hp) of convergence.

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