Three methods to solve two classes of integral equations of the second kind are introduced in
this paper. Firstly, two Kantorovich methods are proposed and examined to numerically solving an integral
equation appearing from mathematical modeling in biology. We use a sequence of orthogonal ﬁnite rank
projections. The ﬁrst method is based on general grid projections. The second one is established by using
the shifted Legendre polynomials. We present a new convergence analysis results and we prove the associated
theorems. Secondly, a new Nystr¨om method is introduced for solving Fredholm integral equation of the second kind.