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Dehghan, M. (2005) On the solution of an initial-boundary value problem that combines Neumann and integral condition for the wave equation. Numerical Methods for Partial Differential Equations, 21, 24-40.
http://dx.doi.org/10.1002/num.20019

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• 标题: 一维Sine-Gordon方程四阶紧致有限体积方法A Fourth-Order Compact Finite Volume Scheme for 1D Sine-Gordon Equations

  作者: 刘盎然, 高巍, 李宏

  关键字: Sine-Gordon, 有限体积紧格式, Runge-Kutta方法Sine-Gordon, Compact Method, Finite Volume Method, Runge-Kutta Method

  期刊名称: 《Advances in Applied Mathematics》, Vol.4 No.3, 2015-08-18

  摘要: 本文提出一个高阶方法来数值求解非线性Sine-Gordon方程。空间离散上应用四阶的紧致有限体积格式，时间离散应用三阶SSP Runge-Kutta (RK)方法。数值实验表明该算法是求解一维Sine-Gordon方程的较为高效的方法。 In this work, we propose a compact finite volume method for solving the one-dimensional nonlinear sine-Gordon equation. The third-order SSP Runge-Kutta (RK) scheme is used for temporal disretization. Numerical experiments show that the present scheme is an efficient algorithm for solving the one-dimensional Sine-Gordon equation.