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

Summary.

In this study, a new iteration of order four is introduced on Banach spaces. We establish, using a new system of recurrence relations, a semilocal convergence theorem under the same conditions as for Newton's method. Next, we use this theorem to obtain the existence of a unique solution of a Chandrasekhar equation. Finally, this solution is approximated by the fourth-order method.