Numerical Differentiation

  • Philipp O. J. Scherer
Part of the Graduate Texts in Physics book series (GTP)


For more complex problems analytical derivatives are not always available and have to be approximated by numerical methods. Numerical differentiation is also very important for the discretization of differential equations. The simplest approximation uses a forward difference quotient and is not very accurate. A symmetric difference quotient improves the quality. Even higher precision is obtained with the extrapolation method. Approximations to higher order derivatives can be obtained systematically with the help of polynomial interpolation.


  1. 217.
    L.F. Richardson, Philos. Trans. R. Soc. Lond. Ser. A 210, 307–357 (1911) CrossRefGoogle Scholar

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© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Philipp O. J. Scherer
    • 1
  1. 1.Physikdepartment T38Technische Universität MünchenGarchingGermany

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