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

作者：Xie Wen Jing; Lin Fu Rong^*

来源：Applied Numerical Mathematics, 2009, 59(7): 1709-1719.

DOI：10.1016/j.apnum.2009.01.009

• Integral equation
• Polynomial interpolation
• Approximate matrix
• Residual correction scheme

In this paper we consider numerical solution methods for two dimensional Fredholm integral equation of the second kind
f(x, y) - (-1)integral(1) (-1)integral(1) a(x, y, u, v)f(u, v)du dv = g(x, y), (x, y) is an element of vertical bar-1, 1 vertical bar x vertical bar-1, 1 vertical bar,
where a(x, y, u, v) is smooth and g(x, y) is in L(2)vertical bar-1, 1 vertical bar(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.

• 出版日期2009-7
• 单位汕头大学