A fast numerical solution method for two dimensional Fredholm integral equations of the second kind

Authors:
Wen-Jing Xie;Fu-Rong Lin
Affiliations:
Department of Mathematics, Shantou University, Shantou Guangdong 515063, China;Department of Mathematics, Shantou University, Shantou Guangdong 515063, China
Venue:
Applied Numerical Mathematics
Year:
2009

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Abstract

In this paper we consider numerical solution methods for two dimensional Fredholm integral equation of the second kindf(x,y)-@!-11@!-11a(x,y,u,v)f(u,v)dudv=g(x,y),(x,y)@?[-1,1]x[-1,1], where a(x,y,u,v) is smooth and g(x,y) is in L^2[-1,1]^2. We discuss polynomial interpolation methods for four-variable functions and then use the interpolating polynomial to approximate the kernel function a(x,y,u,v). Based on the approximation we deduce fast matrix-vector multiplication algorithms and efficient preconditioners for the above two dimensional integral equations. The residual correction scheme is used to solve the discretization linear system.