四阶抛物问题基于降维格式的一种差分谱逼近  

Differential spectral approximation based on a dimensionality reduction for the fourth-order parabolic problem

作　　者：王军林 胡小平 安静 WANG Junlin;HU Xiaoping;AN Jing(School of Mathematical Science,Guizhou Normal University,Guiyang 550025,Guizhou,China)

机构地区：[1]贵州师范大学数学科学学院,贵州贵阳550025

出　　处：《山东大学学报(理学版)》2025年第2期114-126,共13页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11661022,12061023)。

摘　　要：提出了球域上四阶抛物问题基于降维格式的一种差分谱逼近。将四阶抛物问题转化为球坐标系下的等价形式,利用Laplace-Beltrami算子的性质和球谐函数的正交性,进一步分解为一系列解耦的一维四阶抛物问题。基于每个一维四阶抛物问题,建立了其全离散格式,并且证明了全离散格式的稳定性和逼近解的误差估计。给出一些数值算例,数值结果表明差分谱逼近算法是稳定的和收敛的。This paper presents a differential spectral approximation for a fourth-order parabolic problem on a spherical domain based on a dimension reduction scheme.The fourth-order parabolic problem is transformed into an equivalent form in the spherical coordinates.By utilizing the properties of the Laplace-Beltrami operator and the orthogonality of the spherical harmonic functions,the problem is further decomposed into a series of decoupled one-dimensional fourth-order parabolic problems.Based on each onedimensional fourth-order parabolic problem,its fully discrete scheme is established,and its stability and error estimation of the approximate solution are proved.Some numerical examples are given.The numerical results are shown that the differential spectral approximation algorithm is stable and convergent.

关 键 词：四阶抛物问题 降维 差分谱格式 稳定性及误差估计 球域 

分 类 号：O241.82[理学—计算数学]