
Elena Bautu, Elena Pelican. Numerical Solution For Fredholm First Kind Integral Equations Occurring In Synthesis of Electromagnetic Fields. Romanian Journal of Physics, 52 (34), pp. 245256, 2007.
Abstract:
It is known that Fredholm integral equations of the first kind
int_0^1{k(s,t)x(t)}{mathrm d}t=y(s), sin [0,1]
with the kernel frac{(st)^m}{[1(st)^2]^n} occur when solving with problems of synthesis of electrostatic and magnetic fields (m, n  nonnegative rational numbers). This paper presents two approaches for solving such an equation. The first one involves discretization by a collocation method and numerical solution using an approximate orthogonalization algorithm. The second method is based on a nature inspired heuristic, namely genetic programming. It applies geneticallyinspired operators to populations of potential solutions in the form of program trees, in an iterative fashion, creating new populations while searching for an optimal or nearoptimal solution to the problem at hand. Results obtained in experiments are presented for both approaches.
Keywords:
inverse problems, integral equation of the first kind, genetic programming
URL:
http://www.nipne.ro/rjp/2007_52_34/0245_0257.pdf
Posted by
Elena Bautu
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