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


In this chapter we intend to explore several numerical techniques for fitting a known function to a linear or nonlinear differential equation. This technique, known as quasilinearization, makes specific use of the underlying structure of the linear differential equation allowing us to approximate, numerically, both initial conditions and system parameters associated with the selected differential equation.


Nonlinear Differential Equation Linear Differential Equation Quadratic Convergence Time Vary Coefficient Approximation Table 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Bibliography and Comments

  1. Bellman, R.:1970, Methods of Nonlinear Analysis, vol I & II, Academic Press, N.Y.Google Scholar
  2. Bellman, R. and R. Kalaba:1965, Quasi-linearization and Nonlinear Boundary Value Problems, American Elsevier Publishing Co, N.Y.Google Scholar
  3. Kalaba, R.:1954, “On Nonlinear Differential Equations, the Maximum Operation and Monotone Convergence” J. Math. Mech, 8, 519–574Google Scholar
  4. Roth, R.:1966, “Data Unscrambling: Studies in Segmental Differential Approximation”, JMAA, 14,1, 5–22Google Scholar
  5. Bellman,B. Gluss and R.S. Roth,:1964, “On the Identification of Systems and the Uscrambling of Data: Some problems suggested by Neurophysiology” Proc.Nat.Acad.Sci, 52, 1239–1240MathSciNetCrossRefGoogle Scholar
  6. Bellman, R., B. Gluss and R.S. Roth:1965, “Segmental Differential Approximation and the ‘Black Box’ Problem” JMAA, 12, 191–204MathSciNetGoogle Scholar
  7. Bellman, R. and R.S. Roth,:1966, “A Technique for the Analysis of a Broad Class of Biological Systems”, Bionics Symp, Gordon and BreachGoogle Scholar
  8. Bellman R, and R.S. Roth,:1966, “Segmental Differential Approximation and Biological Systems:An Analysis of a Metabolic Process”, J. Theor. Biol. 11, 168–176CrossRefGoogle Scholar
  9. Roth, R.S. and M.M, Roth,:1969, “Data Unscrambling and the Analysis of Inducible Enzyme Synthesis”, Math. Biosci, 5, 57–92.CrossRefGoogle 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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