泊松方程的有限差分思想启发式教学研究  

On Heuristic Teaching of Finite Difference for Poisson Equation

作　　者：高娅莉 GAO Yali(School of Mathematics and Statistics,Northwestern Polytechnical University,Xi'an 710129,China)

机构地区：[1]西北工业大学数学与统计学院,陕西西安710129

出　　处：《高等数学研究》2024年第4期56-60,共5页Studies in College Mathematics

基　　金：国家自然科学基金(N0.12371406)。

摘　　要：在偏微分方程数值解教学中,以泊松方程的有限差分方法为例,利用问题导向的启发式教学方法,基于差分思想,构建了四种以网格节点上的值为自由度的代数方程组,把微分方程的定解问题转化为求解代数方程组的问题,结合程序设计提高教学质量.In teaching numerical solutions for partial differential equations,specifically the finite difference method for Poisson's equation,a problem-oriented heuristic approach is used.Based on the concept of differences,four types of algebraic equations are constructed with grid node values as degrees of freedom.This transforms the problem into solving these algebraic equations.Combining this with program design enhances teaching quality.

关 键 词：数值解 偏微分方程 广义有限差分法 有限体积元方法 

分 类 号：G420[文化科学—课程与教学论] O241.8[文化科学—教育学]