Quadrature methods for Symm's integral equation on polygons

1997 ◽  
Vol 17 (4) ◽  
pp. 643-664 ◽  
Author(s):  
J Elschner
Keyword(s):  
Integral Equation ◽  
Quadrature Methods ◽  
Symm’S Integral Equation

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.

scholarly journals On the Stability of Numerical Methods for Nonlinear Volterra Integral Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-18 ◽  
Author(s):  
E. Messina ◽  
Y. Muroya ◽  
E. Russo ◽  
A. Vecchio
Keyword(s):  
Integral Equation ◽  
Numerical Methods ◽  
Numerical Solution ◽  
Volterra Integral Equation ◽  
Linear Part ◽  
Approximate Solutions ◽  
Constant Sign ◽  
Quadrature Methods ◽  
Decay Of Solutions ◽  
The Stability

Here we investigate the behavior of the analytical and numerical solution of a nonlinear second kind Volterra integral equation where the linear part of the kernel has a constant sign and we provide conditions for the boundedness or decay of solutions and approximate solutions obtained by Volterra Runge-Kutta and Direct Quadrature methods.

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