2026 , Volume 31, № 5, p.38-53

This study investigates a state-dependent Chandrasekhar integral equation and establishes the existence and uniqueness of a continuous solution via the Banach fixed- point theorem in an appropriate Lipschitz space. Building upon this analytical foundation, we propose a robust numerical scheme that integrates successive approximation techniques with suitable quadrature rules. A comprehensive convergence analysis is carried out, including an implicit power-series representation of the solution and explicit bounds on both iteration and quadrature errors. The effectiveness of the proposed method is illustrated through several representative examples, encompassing linear, nonlinear, and strongly nonlinear models. The numerical results demonstrate rapid convergence, strong stability, and high accuracy, underscoring the approach’s capability for the efficient computation of state-dependent integral equations arising inradiative transfer and related applications.