Volume 11, Issue 1
Regularised Finite Difference Methods for the Logarithmic Klein-Gordon Equation

East Asian J. Appl. Math., 11 (2021), pp. 119-142.

Published online: 2020-11

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• 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 $\mathcal{O}(ε)$.

• Keywords

Logarithmic Klein-Gordon equation, regularised logarithmic Klein-Gordon equation, finite difference method, error estimate, convergence order.

35Q40, 65M15, 81Q05

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@Article{EAJAM-11-119, author = {Jingye and Yan and and 9660 and and Jingye Yan and Hong and Zhang and and 9661 and and Hong Zhang and Xu and Qian and and 9662 and and Xu Qian and Songhe and Song and and 9663 and and Songhe Song}, title = {Regularised Finite Difference Methods for the Logarithmic Klein-Gordon Equation}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {11}, number = {1}, pages = {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 $\mathcal{O}(ε)$.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.140820.250820 }, url = {http://global-sci.org/intro/article_detail/eajam/18416.html} }
TY - JOUR T1 - Regularised Finite Difference Methods for the Logarithmic Klein-Gordon Equation AU - Yan , Jingye AU - Zhang , Hong AU - Qian , Xu AU - Song , Songhe JO - East Asian Journal on Applied Mathematics VL - 1 SP - 119 EP - 142 PY - 2020 DA - 2020/11 SN - 11 DO - http://doi.org/10.4208/eajam.140820.250820 UR - https://global-sci.org/intro/article_detail/eajam/18416.html KW - Logarithmic Klein-Gordon equation, regularised logarithmic Klein-Gordon equation, finite difference method, error estimate, convergence order. AB -

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 $\mathcal{O}(ε)$.

Jingye Yan, Hong Zhang, Xu Qian & Songhe Song. (2020). Regularised Finite Difference Methods for the Logarithmic Klein-Gordon Equation. East Asian Journal on Applied Mathematics. 11 (1). 119-142. doi:10.4208/eajam.140820.250820
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