Solution of Approximate Equations

  • Richard E. Bellman
  • Robert S. Roth
Part of the Mathematics and Its Applications book series (MAIA, volume 26)


In this chapter we wish to explore some of the ideas surrounding approximate equations. The basic idea is the following: if we are confronted with a nonlinear differential equation whose solution is unknown, then we would like to replace this equation with a set, one or more, of approximating equations whose solutions are known. Our goal is to see if we can obtain an approximate solution to the nonlinear system by exact solutions to the approximating equation. Since we are, in fact, approximating one differential equation by a set of others, this chapter considers the interrelations between them.


Dynamic Program RICCATI Equation Nonlinear Differential Equation Order Differential Equation Approximate Equation 
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Bibliography and Comments

  1. Bellman, R.:1966, Perturbation Techniques in Mathematics, Engineering and Physics, Dover, N.Y.Google Scholar
  2. Bellman, R.:1978, “On the Solution of Approximate Equations”, Nonlinear Anal., Theory, Methods and Appl. 3,5, 717–719Google Scholar
  3. Bellman, R. and Roth, R.:1969, “Curve Fitting by Segmented Straight Lines”, J. Amer. Stat. Assoc. 64, 1077–1084MathSciNetCrossRefGoogle Scholar
  4. Roth, R.:1966, “Data Unscrambling: Studies in Segmental Differential Approximation”, JMAA, 14, 5–22Google Scholar
  5. Bellman, R.:1957, Dynamic Programming, Princeton University Press, Princeton, N.J.Google Scholar
  6. Bellman, R. and Dryfus, S.:1963, Applied Dynamic Programming,Princeton University Press, Princeton, N.J.Google Scholar

Copyright information

© D Reidel Publishing Company 1986

Authors and Affiliations

  • Richard E. Bellman
    • 1
    • 2
  • Robert S. Roth
    • 3
  1. 1.Department of Electrical EngineeringUniversity of Southern CaliforniaLos AngelesUSA
  2. 2.Center for Applied MathematicsThe University of GeorgiaAthensUSA
  3. 3.BostonUSA

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