An Energy Conserving Numerical Scheme for the Klein-Gordon Equation with Cubic Nonlinearity

被引：2

作者：

Alzaleq, Lewa ^{[1
]}

Manoranjan, Valipuram ^{[2
]}

机构：

[1] Al al Bayt Univ, Dept Math, Fac Sci, Mafraq 25113, Jordan

[2] Washington State Univ, Dept Math & Stat, Pullman, WA 99164 USA

来源：

FRACTAL AND FRACTIONAL | 2022年 / 6卷 / 08期

关键词：

Klein-Gordon equation; finite difference scheme; discrete energy; convergence; stability; TIME;

D O I：

10.3390/fractalfract6080461

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we develop a numerical scheme that conserves the discrete energy for solving the Klein-Gordon equation with cubic nonlinearity. We prove theoretically that our scheme conserves not just discrete energy, but also other energy-like discrete quantities. In addition, we prove the convergence and the stability of the scheme. Finally, we present some numerical simulations to demonstrate the performance of our energy-conserving scheme.

引用

页数：18

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