Stability analysis of the numerical Method of characteristics applied to a class of energy-preserving hyperbolic systems. Part I: Periodic boundary conditions

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:356

Article

Lakoba, T. I.¹  Deng, Z.¹ 

[1] Univ Vermont, Dept Math & Stat, 16 Colchester Ave, Burlington, VT 05401 USA

关键词: Method of characteristics;    Coupled-wave equations;    Numerical instability;   

DOI  :  10.1016/j.cam.2019.01.027

来源: Elsevier

【 摘 要 】

We study numerical (in)stability of the Method of characteristics (MoC) applied to a system of non-dissipative hyperbolic partial differential equations (PDEs) with periodic boundary conditions. We consider three different solvers along the characteristics: simple Euler (SE), modified Euler (ME), and Leap-frog (LF). The two former solvers are well known to exhibit a mild, but unconditional, numerical instability for non-dissipative ordinary differential equations (ODES). They are found to have a similar (or stronger, for the MoC-ME) instability when applied to non-dissipative PDEs. On the other hand, the LF solver is known to be stable when applied to non-dissipative ODEs. However, when applied to non-dissipative PDEs within the MoC framework, it was found to have by far the strongest instability among all three solvers. We also comment on the use of the fourth-order Runge-Kutta solver within the MoC framework. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free