A NOTE ON MONOTONE CONVERGENCE TO SOLUTIONS OF FIRST ORDER DIFFERENTIAL EQUATIONS

Abstract

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.

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Document Details

Document Type
Technical Report
Publication Date
Jan 16, 1957
Accession Number
AD0606263

Entities

People

  • Richard E. Bellman

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Analogs
  • Computer Programming
  • Convergence
  • Differential Equations
  • Dynamic Programming
  • Equations
  • Inequalities
  • Intervals
  • Mathematics
  • Sequences
  • Standards

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Statistical inference.