Stability analysis of discontinuous Galerkin method for stiff Volterra functional differential equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:475

Article

Zhang, Gengen¹  He, Guoman²  Dai, Xinjie³ 

[1] Guangxi Normal Univ, Sch Math & Stat, Guilin 541004, Peoples R China

[2] Hunan Univ Commerce, Sch Math & Stat, Changsha 410205, Hunan, Peoples R China

[3] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China

关键词: Stability;    Discontinuous Galerkin method;    Delay;    Volterra functional differential equation;    Stiff problem;   

DOI  :  10.1016/j.jmaa.2019.03.013

来源: Elsevier

【 摘 要 】

This paper concerns the nonlinear stability properties of discontinuous Galerkin (DG) method for stiff Volterra functional differential equations (VFDEs). We derive that the DG method leads to global and analogously asymptotical stability for VFDEs, and it is shown that the perturbations of the numerical solution are controlled by the initial perturbations. This general results provide unified theoretical treatment for numerical stability analysis of Volterra integro-differential equations (VIDEs) with constant or variable delay, delay differential equations (DDEs), ordinary differential equations (ODEs) and so on. Numerical examples are given to confirm our theoretical results. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free