Document Type
Article
Publication Date
1-2023
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.
Recommended Citation
Aluthge, A. and Sarra, S.A. (2023) A Filtered Milne-Simpson ODE Method with Enhanced Stability Properties. Journal of Applied Mathematics and Physics, 11, 192-208. https://doi.org/10.4236/jamp.2023.111013
Comments
The copy of record is available at Copyright © 2023 The Authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0).