Robust projection method for Fredholm integral equation of the second kind.

The projection method based on the Schauder basis expansion for solving the Fredholm integral equation of the second kind is investigated. (1) It is shown that any given finite linearly independent function set in Lp[0, 1] can be extended as a Schauder basis. The truncation of the dual Schauder bases is then used to form the projection in approximating the kernel. (2) With the finite rank approximation, the use of the Sherman-Morrison-Woodbury formula achieves efficient implementation. The computation is successive when dimension of projection space increases. Numerical experiments demonstrate the robustness of the Schauder basis expansion. [ABSTRACT FROM AUTHOR]