A Note on Monotone Convergence to Solutions of First Order Differential Equations

摘要

The purpose of this brief note was to show that one can obtain a monotone increasing sequence of approximations to the solution of the differential equation du/dt = phi(u,t), u(o) = c, provided that one assume that phi(u,t) is a twice differentiable convex function of u in some t-interval (o,t sub 0). Similarly, monotone decreasing sequences can be obtained if phi is concave. (Author)