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Gragg, W.B. (1963) Re-Peated Extrapolation to the Limit in the Numerical Solution of Ordinary Differential Equations. Ph.D. Thesis, University of California, Los Angeles (UCLA), Los Angeles, 1-111.

has been cited by the following article:

• TITLE: A Filtered Milne-Simpson ODE Method with Enhanced Stability Properties

  AUTHORS: Ari Aluthge, Scott A. Sarra

  KEYWORDS: Ordinary Differential Equations, Numerical Methods, Weak Instability

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.1, January 31, 2023

  ABSTRACT: The Milne-Simpson method is a two-step implicit linear multistep method for the numerical solution of ODEs that obtains the theoretically highest order of convergence for such a method. The stability region of the method is only an interval on the imaginary axis and the method is classified as weakly stable which causes non-physical oscillations to appear in numerical solutions. For this reason, the method is seldom used in applications. This work examines filtering techniques that improve the stability properties of the Milne-Simpson method while retaining its fourth-order convergence rate. The resulting filtered Milne-Simpson method is attractive as a method of lines integrator of linear time-dependent partial differential equations.