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>> Românã

Elena Bautu, Elena Pelican. Numerical Solution For Fredholm First Kind Integral Equations Occurring In Synthesis of Electromagnetic Fields. Romanian Journal of Physics, 52 (3-4), pp. 245-256, 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{(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.

Keywords: inverse problems, integral equation of the first kind, genetic programming


Posted by Elena Bautu


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