全直线上四阶方程的Laguerre-Legendre-Laguerre复合谱逼近  

Composite Laguerre-Legendre-Laguerre Spectral Method for the Fourth-order Equation on the Whole Line

作　　者：叶小华[1] 庄清渠[2] YE Xiaohua;ZHUANG Qingqu(School of General Education,Liming Vocational University,Quanzhou Fujian 362000,China;School of Mathematical Sciences,Huaqiao University,Quanzhou Fujian 362021,China)

机构地区：[1]黎明职业大学通识教育学院,福建泉州362000 [2]华侨大学数学科学学院,福建泉州362021

出　　处：《佳木斯大学学报（自然科学版）》2022年第2期159-162,共4页Journal of Jiamusi University：Natural Science Edition

基　　金：福建省自然科学基金(2021J01306);国家自然科学基金(11771083)。

摘　　要：针对全直线上的四阶方程构造了Laguerre-Legendre-Laguerrre复合谱逼近格式.将全直线剖分为三个子区间,在每个子区间上用不同的谱方法对进行求解.通过构造恰当的基函数来保证交面的连续性,将问题分裂为规模较小的子问题进行求解.通过数值算例说明方法的高精度,与纯Hermite谱方法逼近结果比较说明该方法的有效性.A composite Laguerre-Legendre-Laguerre spectral method is presented to approximate the fourth-order equations on the whole line.The whole line is decomposed into three sub-domains.Different spectral methods are used in each sub-domain.Appropriate basis functions are constructed to ensure the continuity between the elemental-faces.The problem is decomposed into some smaller subproblems and thus solved efficiently.Numerical results show the spectral accuracy of the method.The advantage of the method is also demonstrated by a numerical comparison with the pure Hermite method.

关 键 词：Laguerre-Legendre-Laguerre复合谱方法 全直线 四阶方程 

分 类 号：O241.8[理学—计算数学]