RLW方程六阶空间精度的线性守恒差分格式-《集美大学学报（自然科学版）》

文章信息/Info

Title:: A Linear Conservative Difference Scheme with Six-Order Spatial Accuracy for the RLW Equation

作者:: 付天浩1; 2; 王晓峰1; 2; 刘佳垚1; 2; 付瑶1; 2; 1.闽南师范大学数学与统计学院, 福建漳州 363000;2.福建省粒计算及其重点实验室, 福建漳州 363000

Author(s):: FU Tianhao1; 2; WANG Xiaofeng1; 2; LIU Jiayao1; 2; FU Yao1; 2; 1.School of Mathematics and Statistics,Minnan Normal University,Zhangzhou 363000，China;2.Fujian Key Laboratory of Granular Computing and Applications,Zhangzhou 363000，China

Keywords:: regularised long wave (RLW) equation; linear difference scheme; sixth-order accuracy; convergence; stability

摘要:: 对正则长波(RLW)方程建立一个具有高精度的三层隐式差分格式,该格式具有二阶时间精度和六阶空间精度,且在离散意义下能够合理地模拟原问题的质量守恒和能量守恒。采用离散能量法和Von Neumann分析法证明了所构造数值格式的收敛性和稳定性。数值算例验证了所建格式的有效性,且该格式明显优于其他数值格式。

Abstract:: A three-level implicit difference scheme with high-order spatial accuracy is proposed for the regularised long wave (RLW) equation.The proposed scheme has second-order temporal accuracy and sixth-order spatial accuracy.Also,the scheme can reasonably simulate the mass conservation and energy conservation of the original problem in discrete sense.The convergence and stability of the proposed numerical scheme are proved using the discrete energy method and Von Neumann analysis.Numerical example is given to verify the validity of the proposed scheme and the scheme is obviously better than other numerical schemes.