non-classical sinc collocation method for approximating hallen's integral equation

In this paper, we propose a novel numerical method for solving hallen's integral equation, based on the sinc collocation approximation. the key innovation of our approach lies in the incorporation of weight functions into the traditional sinc-expansion framework. by leveraging the properties of sinc collocation, we transform hallen's integral equation into a system of algebraic equations, which can be solved efficiently.  our method involves discretizing the singular kernel of hallen's integral equation and then applying the sinc approximation. additionally, we provide a detailed analysis of the convergence and error estimation of the proposed method. numerical results are presented for three distinct values of $lambda$ and $l$, as well as for three different weight functions: $w(t)=1+sin(pi t)$, $w(t)=1+cos(frac{pi t}{2})$ and $w(t)=1+t$.