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Gragg, W.B. (1963) Re-peated Extrapolation to the Limit in the Numerical Solution of Ordinary Differential Equations. PhD Thesis, UCLA.

has been cited by the following article:

• TITLE: Filtered Leapfrog Time Integration with Enhanced Stability Properties

  AUTHORS: Ari Aluthge, Scott A. Sarra, Roger Estep

  KEYWORDS: Leapfrog Method, Computational Mode, Weak Stability, Method of Lines, Numerical Weather Prediction

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.4 No.7, July 28, 2016

  ABSTRACT: The Leapfrog method for the solution of Ordinary Differential Equation initial value problems has been historically popular for several reasons. The method has second order accuracy, requires only one function evaluation per time step, and is non-dissipative. Despite the mentioned attractive properties, the method has some unfavorable stability properties. The absolute stability region of the method is only an interval located on the imaginary axis, rather than a region in the complex plane. The method is only weakly stable and thus exhibits computational instability in long time integrations over intervals of finite length. In this work, the use of filters is examined for the purposes of both controlling the weak instability and also enlarging the size of the absolute stability region of the method.