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Numerical Solution For Fredholm First Kind Integral Equations Occurring In Synthesis of Electromagnetic Fields

Domenii publicaţii > Ştiinţe informatice + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: Elena Bautu, Elena Pelican

Editorial: Romanian Journal of Physics, 52 (3-4), p.245-256, 2007.


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{(s-t)^m}{[1-(s-t)^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 genetically-inspired 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 near-optimal solution to the problem at hand. Results obtained in experiments are presented for both approaches.

Cuvinte cheie: inverse problems, integral equation of the first kind, genetic programming // inverse problems, integral equation of the first kind, genetic programming