Regularised Finite Difference Methods for the Logarithmic Klein-Gordon Equation

被引：4

作者：

Yan, Jingye ^{[1
]}

Zhang, Hong ^{[1
]}

Qian, Xu ^{[1
]}

Song, Songhe ^{[1
,2
]}

机构：

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

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

来源：

EAST ASIAN JOURNAL ON APPLIED MATHEMATICS | 2021年 / 11卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Logarithmic Klein-Gordon equation; regularised logarithmic Klein-Gordon equation; finite difference method; error estimate; convergence order; PSEUDOSPECTRAL METHOD; SCHRODINGER-EQUATION; NUMERICAL-METHODS; GLOBAL-SOLUTIONS; MODEL; SOLITONS; SCHEMES; SYSTEM;

D O I：

10.4208/eajam.140820.250820

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 < epsilon < 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 O(epsilon).

引用

页码：119 / 142

页数：24

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