An almost monotone approximation for a nonlinear two-point boundary value problem

Almost monotone approximation is proposed for nonlinear two-points problem. A general framework is given for studying the existence and uniqueness of numerical solutions. A discrete approximation with high accuracy is constructed. Nonlinear Jacobi iteration and Gauss-Seidel iteration are introduced to save work. The continuous approximation is also considered. The numerical results show the advantages of such an approach.