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 - <p style="text-align: justify;">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 $0 &lt;&nbsp;ε&nbsp;≪ 1$. 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 $\mathcal{O}(ε)$.</p>