Numerical Solution of a Two-Point Boundary-Value Problem for a System of Linear Differential Equations with Nonlinear Two-Dimensional Spectral Parameter

Abstract

We study the possibility of application of the implicit-function method to the solution of two-point boundary-value problems for systems of linear differential equations with nonlinear two-dimensional spectral parameters appearing in the coefficients of this system and boundary conditions. We also substantiate the convergence of the approximate solutions of discretized problems to the exact solutions of the original problem.