抛物方程的Legendre Galerkin谱配置最小二乘法  

Legendre Galerkin spectral collocation least square method for parabolic equation

作　　者：胡玉巧 覃永辉 范友康 HU Yuqiao;QIN Yonghui;FAN Youkang(School of Mathemectics and Computing Science,Guilin University of Electronic Technology,Guilin 541004,China;Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation,Guilin University of Electronic Technology,Guilin 541004,China;Guangxi Key Laboratory of Cryptography and Information Security,Guilin University of Electronic Technology,Guilin 541004,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004 [2]桂林电子科技大学广西高校数据分析与计算重点实验室,广西桂林541004 [3]桂林电子科技大学广西密码学与信息安全重点实验室,广西桂林541004

出　　处：《桂林电子科技大学学报》2021年第1期55-60,共6页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(11701119,11961010,11961012);广西自然科学基金(2017GXNSFBA198053);广西科技基地和人才专项(2018AD19051);桂林电子科技大学研究生教育创新计划(2020YCXS086)。

摘　　要：为了进一步提高求解抛物型方程的数值精度,针对一种抛物型方程,研究了Legendre-Galerkin谱配置最小二乘法。通过引入一个通量,将原问题转化为等价的一阶系统,并定义其半离散的最小二乘函数。空间上采用Legendre Galerkin方法,时间方向采用差分方法对时间变量进行离散,用Legendre/Chebyshev-Gauss-Lobatto配置法对右端源项进行离散。该方法导出的代数方程组的系数矩阵具有对称正定特点。数值实验结果表明,该方法具有有效性和高阶谱精度。In order to further improve the numerical accuracy of solving parabolic equations,this paper studies the Legendre Galerkin spectral collocation least square method for a parabolic equation.By introducing a flux,the original problem is transformed into an equivalent first-order system,and its corresponding semi-discrete least square function is defined.The Legendre Galerkin method is used in space,the time variable is discretized by the difference method in the time direction,and the right-hand side term is treated by the interpolation with the Legendre/Chebyshev-Gauss-Lobatto collocation method.The coefficient matrix of algebraic equations derived by this method has the characteristics of symmetric positive definite.Numerical results show that the method is effective and has high order spectral accuracy.

关 键 词：抛物方程 最小二乘 Legendre Galerkin Legendre/Chebyshev-Gauss-Lobatto点 

分 类 号：O241.82[理学—计算数学]