On the application of a fourth-order two-point method to Chandrasekhar's integral equation (Q5945045)

The authors introduce a new iteration of order four on Banach spaces. By using a new system of recurrence relations, they establish a semi-local convergence theorem under the same conditions as for Newton's method. They use the convergence theorem to prove the existence and uniqueness of solutions of a Chandrasekhar equation. Equations of this type arise in the theories of radiative transfer, neutron transfer and in the kinetic theory of gases. Finally, the authors construct an arithmetic model of the Chandrasekhar equation and show that the solution of the finite dimension problem is approximated by the fourth-order iterative method. This solution is interpolated to approximate the solution function of the Chandrasekhar equation.