A note on monotone convergence to solutions of first-order differential equations.

by Richard Ernest Bellman

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An attempt to show that a monotone increasing sequence of approximation can be obtained to the solution of the differential equation du/dt = 0(u,t),u(O) = c. It is assumed that 0(u,t) is a twice differentiable convex function of u in some t-interval [O,to]. Similarly, monotone decreasing sequences can be obtained if 0 is concave. (0 represents a small circle with a long vertical line across it; O represents a zero; o represents a sub script)

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