Accurate three-point difference schemes for second-order monotone ordinary differential equations and their implementation (Q5954369)

The author analyzes the existence of accurate three-point difference schemes for nonlinear monotone boundary value problems in the case without constraints on the mesh size \(h\) of the grid \({\omega}_h\). An implementation of accurate three-point difference schemes in terms of \(m\)th-order accuracy is developed and justified, which allows one to apply three-point difference schemes to problems with large Lipschitz constants.