Approximation theory 3 Boundary value problems 3 Convergence of numerical methods 3 Differentiation (calculus) 3 Discretized Newton method 3 Function evaluation 3 Functional elimination 3 Iterative methods 3 Jacobian matrix 3 Mathematical models 3 Matrix algebra 3 Monotone discrete Newton iterations 3 Monotone sequences 3 Nonlinear equations 3 Nonlinear systems 3 Order convex functions 3 Theorem proving 3