Discrete Variational Theory

  • Calvin D. Ahlbrandt
  • Allan C. Peterson
Part of the Kluwer Texts in the Mathematical Sciences book series (TMS, volume 16)


We begin this chapter by describing a simple fixed endpoint discrete variational problem. We initially consider fixed step sizes of length 1. However, in Section 4.7 we will let the step sizes be of variable length. Assume f(t, y, r) for each t in the discrete interval [a + 1, b + 2] is of class C 2 with respect to the components of the n dimensional vector variables y and r. We define a set of admissible functions by
$$\mathcal{F} = \{ y:[a,b + 2] \to {{R}^{n}}:y(a) = \alpha ,\quad y(b + 2) = \beta \}$$
where α and β are given column n vectors.


Hamiltonian System Implicit Function Theorem Jacobi Equation Local Extremum Transversality Condition 
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Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • Calvin D. Ahlbrandt
    • 1
  • Allan C. Peterson
    • 2
  1. 1.University of MissouriUSA
  2. 2.University of NebraskaUSA

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