正交配置方法求解一维拟线性抛物方程  

Orthogonal collocation method for one-dimensional quasi-linear parabolic equations

作　　者：王佩臣[1] 张志维 樊玉环[1] 张可为[1] WANG Peichen;ZHANG Zhiwei;FAN Yuhuan;ZHANG Kewei(College of Science,Heilongjiang Institute of Technology,Harbin 150050,China)

机构地区：[1]黑龙江工程学院理学院,哈尔滨150050

出　　处：《黑龙江工程学院学报》2022年第6期1-4,共4页Journal of Heilongjiang Institute of Technology

基　　金：黑龙江省自然科学基金项目(QC2016088,QC2011C020)。

摘　　要：提出一个新的方法求解一维拟线性抛物方程,使用Chebyshev Gauss Lobatto节点和配点公式计算谱差分矩阵,用A稳定的对角隐式龙格库塔法(DIRK)求解常微分方程组。首先采用正交配置法对一维拟线性抛物方程进行空间离散,得到一个常微分方程组,然后使用对角隐式龙格库塔法求解常微分方程组。对数值解和精确解进行比较,数值结果证实该方法有很高的精度和稳定性。This paper presents a new method for solving of the one-dimension quasi-linear parabolic equation. by using the collocation formula for calculating spectral differentiation matrix for Chebyshev Gauss Lobatto point and A-stable diagonally implicit Runge Kutta(DIRK) method. Firstly, it discretizes the quasi-linear parabolic equation in one dimensional space with s Orthogonal Collocation Method to obtain a system of ordinary differential equations(ODEs). Secondly, it uses DIRK methods for the numerical integration of the system of ODEs. The numerical results obtained by this way have been compared with the exact solution to show the effciency of the method. The numerical results demonstrate high accuracy and stability of this method.

关 键 词：正交配置方法 对角隐式龙格库塔法 一维拟线性抛物方程 

分 类 号：O241.82[理学—计算数学]