Regularized asymptotic solutions of singularly perturbed integral equations with a higher-order diagonal degeneration of the kernel and the initialization problem

Abstract

An algorithm of the regularization method is developed for singularly perturbed integral equations with a higher-order diagonal degeneration of the kernel. The leading term of the asymptotics is analyzed to solve the problem of initialization (that is, extraction of the class of right-hand sides and kernels of the integral operator for which the exact solution of the original equation tends to some limit function as ε → +0 on the entire time interval, including the boundary-layer zone).