Two regularized energy-preserving finite difference methods for the logarithmic Klein-Gordon equation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:393

Article

Yan, Jingye^1,2  Qian, Xu¹  Zhang, Hong¹  Song, Songhe^1,3 

[1] Natl Univ Def Technol, Coll Arts & Sci, Dept Math, Changsha 410073, Peoples R China

[2] Natl Univ Singapore, Dept Math, Singapore 119076, Singapore

[3] Natl Univ Def Technol, State Key Lab High Performance Comp, Changsha 410073, Peoples R China

关键词: Logarithmic Klein-Gordon equation;    Regularized logarithmic Klein-Gordon equation;    Finite difference method;    Error estimate;    Convergence order;    Energy-preserving;   

DOI  :  10.1016/j.cam.2021.113478

来源: Elsevier

【 摘 要 】

We present and analyze two regularized finite difference methods which preserve energy of the logarithmic Klein-Gordon equation (LogKGE). In order to avoid singularity caused by the logarithmic nonlinearity of the LogKGE, we propose a regularized logarithmic Klein-Gordon equation (RLogKGE) with a small regulation parameter 0 < epsilon << 1 to approximate the LogKGE with the convergence order O(epsilon). To derive the error bound of the two schemes, we combine the energy method, the inverse inequality, with the cut-off technique of the nonlinearity. And we obtain the error estimate at O(h(2) + tau(2)/epsilon(2)) for the two schemes with the mesh size h, the time step tau and the parameter epsilon. Numerical results are reported to support our conclusions. (c) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

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