Monotone methods for solving a boundary value problem of second order discrete system (Q1970055)

A numerical method for the solution of a boundary value problem of a second-order discrete system is considered. A new concept of a pair of upper and lower solutions for this problem is introduced. A comparison of the obtained results with the known ones is given and an existence theorem for a solution is proved in terms of upper and lower solutions. A monotone iterative scheme for the numerical solution of this problem is proposed and the monotone convergence rate of the iteration is compared and analyzed. Numerical results are given.