Year: 2021
Author: Jingye Yan, Hong Zhang, Xu Qian, Songhe Song
East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 1 : pp. 119–142
Abstract
Two regularised finite difference methods for the logarithmic Klein-Gordon equation are studied. In order to deal with the origin singularity, we employ regularised logarithmic Klein-Gordon equations with a regularisation parameter $0 < ε ≪ 1$. Two finite difference methods are applied to the regularised equations. It is proven that the methods have the second order of accuracy both in space and time. Numerical experiments show that the solutions of the regularised equations converge to the solution of the initial equation as $\mathcal{O}(ε)$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.140820.250820
East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 1 : pp. 119–142
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Logarithmic Klein-Gordon equation regularised logarithmic Klein-Gordon equation finite difference method error estimate convergence order.