Numerical analytic method for the case of singular matrices in boundary conditions

A modification of the numerical analytic method of successive approximations is proposed for investigating the existence and constructing solutions of systems of nonlinear ordinary differential equations with two-point linear boundary conditions. The method is tailored to the case where the matrices contained in boundary conditions are singular, but their linear combination is nonsingular.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 5, pp. 673–681, May, 1992.