一维对流扩散方程初始条件反问题的数值求解  

NUMERICAL SOLUTION OF THE INITIAL CONDUCTION INVERSE PROBLEM FOR THE ONE-DIMENSIONAL CONVECTION-DIFFUSION EQUATION

作　　者：韩莹莹 闵涛[2] Han Yingying;Min Tao(Mathematics Teaching Department,City College of Xi'an Jiaotong University,Xi'an 710018;School of Science,Xi'an University of Technology,Xi'an 710054)

机构地区：[1]西安交通大学城市学院数学教学部,西安710018 [2]西安理工大学理学院,西安710054

出　　处：《高等学校计算数学学报》2024年第2期109-120,共12页Numerical Mathematics A Journal of Chinese Universities

摘　　要：1引言对流扩散方程作为一种典型的偏微分方程,描述的是粘性流体运动的非线性方程的线性化模型.因此,对流扩散方程也是一类基本的运动方程.对流扩散方程广泛地应用在流体力学、物理学、环境科学以及电子科学等领域[1-5].就目前的研究,对流扩散方程在具体实际应用时大致可以分为两大类:在已知初边值条件的情况下.The one-dimensional convection-diffusion equation is discretized by the trapezoidal quadrature formula and transformed it into linear discrete equations.On this basis,conjugate gradient least squares algorithm(CGLS)is proposed to invert the initial conduction.The feasibility and effectiveness of the algorithm are verified by specific numerical examples.In addition,the stability estimates of the solutions are given analytically.

关 键 词：对流扩散方程 非线性方程 粘性流体 偏微分方程 运动方程 初边值条件 流体力学 线性化模型 

分 类 号：O241.82[理学—计算数学]