Regularised Finite Difference Methods for the Logarithmic Klein-Gordon Equation

Regularised Finite Difference Methods for the Logarithmic Klein-Gordon Equation

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.

Author Details

Jingye Yan

Hong Zhang

Xu Qian

Songhe Song