Differential Quadrature

  • 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 yet another application of approximation methods, the numerical solution of nonlinear partial differential equations. In many cases all that is desired is a moderately accurate solution at a few points which can be computed rapidly.


Partial Information Differential Quadrature Nonlinear Partial Differential Equation Implicit Solution Reidel Publishing Company 
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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., B.G. Kashef and J. Casti,:1972, “Differential Quadrature: A Tecnhique for the Rapid Solution of Nonlinear Partial Differential Equations”, J. Comp. Phys. 10,1, 40–52MathSciNetzbMATHCrossRefGoogle Scholar
  3. Bellman, R. and B.G. Kashef,:1974, “Solution of the Partial Differential Equation of the Hodgkins-Huxley Model using Differential Quadrature”, Math. Biosci., 19, 1–8MathSciNetzbMATHCrossRefGoogle Scholar
  4. Bellman, R., B.G. Kashef, R. Vasudevan and E. S. Lee,:1975, “Differential Quadrature and Splines”, Computers and Mathematics with Applications,1,3/4, 371–376MathSciNetzbMATHCrossRefGoogle Scholar
  5. Bellman, R., G. Naadimuthu, K.M. Wang, and E,S. Lee,:1984, “Differential Quadrature and Partial Differential Equations” JMAA, 98, 220–235MathSciNetzbMATHGoogle Scholar
  6. Bellman, R. and R.S. Roth,:1979, “Systems Identification with Partial Information”, JMAA, 68,2, 321–333MathSciNetzbMATHGoogle Scholar
  7. Bellman, R. and R.S. Roth,:1979, “A Scanning Technique for Systems Identification”, JMAA, 71,2, 403–411MathSciNetzbMATHGoogle 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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