Brown University Graduate School,
Dissertation Defense Information
Scientific Computing Seminar
Abstract: The solvability of the linear Fredholm integral equation of the first kind, both in discretized and continuous forms, is studied by certain nonlinear techniques. In discretized form, the maximum-entropy solution is developed into an expansion in WKB approximants. The parameters in this expansion are proved to be solutions to a certain nonlinear system of functional equations, incorporating the data of the integral equation. For spectrometric integral equations, this system is shown to be a nonlinear dual iterative search process. In the continuous setting for the integral equation, we show that a variational perturbation of the kernel, in a certain (nonlinearly weighted) dual space, is capable of yielding a direct primal solution. It is also proved that the emerging solution must satisfy an equivalent Urysohn nonlinear integral equation, with a movable bifurcation point.
<--- 2001 Index