A Filtered Milne-Simpson ODE Method with Enhanced Stability Properties  

作　　者：Ari Aluthge Scott A. Sarra Ari Aluthge;Scott A. Sarra(Marshall University, Huntington, WV, USA)

机构地区：[1]Marshall University, Huntington, WV, USA

出　　处：《Journal of Applied Mathematics and Physics》2023年第1期192-208,共17页应用数学与应用物理（英文）

摘　　要：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.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.

关 键 词：Ordinary Differential Equations Numerical Methods Weak Instability 

分 类 号：O17[理学—数学]