Method of accelerated convergence for the construction of solutions of a Noetherian boundary-value problem - Boichuk, О. A.; Chuiko, S. M. (Ukrains’kyi Matematychnyi Zhurnal, 2008)
We study the problem of finding conditions for the existence of solutions of weakly nonlinear Noetherian boundary-value problems for systems of ordinary differential equations and the construction of these solutions. A new iterative procedure with accelerated convergence is proposed for the construction of solutions of a weakly nonlinear Noetherian boundary-value problem for a system of ordinary differential equations in the critical case.