Approximate solutions to the Gardner equation by spectral modified Exponential Time Differencing method
Approximate solutions to the Gardner equation by spectral modified Exponential Time Differencing method
复制标题
谱修正指数时差法近似解加德纳方程
DOI：
10.1016/j.padiff.2022.100310
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发表时间：
2022
影响因子：
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通讯作者：
Chowdhury, Abhinandan
中科院分区：
文献类型：
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作者：
Degon, Leo;Chowdhury, Abhinandan
本文采用基于Kassam和Trefethan提出的指数时间差分方法的谱修正数值格式，对Gardner方程的时空解进行了数值研究。改进格式充分利用围道积分方法的优点，提高了数值稳定性。但它需要明智地选择轮廓路径和适当的离散化，以最小化求解特定的非线性偏微分方程的误差估计。通过一些测试实例，特别是测量离散最大范数误差和全局相对误差，证明了该方案的有效性。相关的守恒定律也通过数值验证，即使在很长的模拟时间后，守恒量从初始值获得非常微小的偏差。
This manuscript is concerned with the numerical study of spatio-temporal solution profiles of the Gardner equation by implementing a well-known spectral modified numerical scheme based on the Exponential Time Differencing method proposed by Kassam and Trefethan. The modified scheme takes full advantage of contour integral method for improving the numerical stability. But it requires judicious selection of contour path with suitable discretization to minimize the error estimates for solving a particular nonlinear partial differential equation. The efficiency of the scheme is demonstrated by testing it on some test examples – especially measuring discrete maximum norm errors and global relative errors. The associated conservative laws are also numerically verified via attaining very insignificant deviation in the conserved quantities from the initial values even after a large simulation time.
与 Boiti-Pempinelli-Tu 谱问题相关的可积孤子层次
DOI：
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发表时间：
2021
期刊：
影响因子：
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作者：
E. Appiah;Solomon Manukure
通讯作者：
Solomon Manukure
具有非热电子和正电子的电子-正电子离子等离子体中的正电子声加德纳孤子和双层
DOI：
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发表时间：
2014
期刊：
影响因子：
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作者：
M. Rahman;M. Alam;A. Mamun
通讯作者：
A. Mamun