The uniqueness of solutions to discrete, vector, two-point boundary value problems

Difference equations which may arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations are investigated and conditions are formulated under which solutions to the discrete problem are unique. Some existence, uniqueness implies existence, and convergence theorems for solutions to the discrete problem are also presented. c © 2003 Elsevier Science Ltd. All rights reserved. Keywords—Uniqueness of solutions, Vector equations, Discrete boundary value problems, Second-order systems of ordinary differential equations.