Aluthge, A., Sarra, S.A. and Estep, R. (2016) Filtered Leapfrog Time Integration with Enhanced Stability Properties. Journal of Applied Mathematics and Physics, 4, 1354-1370.
https://doi.org/10.4236/jamp.2016.47145

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.