Stochastic conformal schemes for damped stochastic Klein-Gordon equation with additive noise

Song, Mingzhan; Xu, Qian; Shen, Tianlong; Song, Songhe

doi:10.1016/j.jcp.2020.109300

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2021

2023

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Cited by 7 publications

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“…For numerical comparison of various numerical methods for the NKGE and the oscillatory NKGE, we refer the reader to [8,13,30,40]. Stochastic conformal Preissman, stochastic conformal discrete gradient and stochastic conformal Euler box schemes for damped stochastic Klein-Gordon equation are presented in [46]. Nevertheless, these methods can not be directly applied to the LogKGE equation (1.1) because of the singularity of the logarithmic non-linearity at the origin.…”

Section: Introductionmentioning

confidence: 99%

Regularised Finite Difference Methods for the Logarithmic Klein-Gordon Equation

Yan¹

2021

EAJAM

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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 < ǫ ≪ 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 (ǫ).

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