Approximation theory 4 Boundary value problems 4 Convergence of numerical methods 4 Differentiation (calculus) 4 Discretized Newton method 4 Function evaluation 4 Functional elimination 4 Iterative methods 4 Jacobian matrix 4 Mathematical models 4 Matrix algebra 4 Monotone discrete Newton iterations 4 Monotone sequences 4 Nonlinear equations 4 Nonlinear systems 4 Order convex functions 4 Theorem proving 4