有限差分方法的教学创新与应用实践
Teaching Innovation and Application Practice of Finite Difference Method

在计算科学与工程领域中，微分方程数值解具有重要的理论性与应用性。本文以信息与计算科学专业所学微分方程数值解课程中有限差分方法的教学为例，探讨教学创新，并从不同角度推导五点差分格式，同时使用Matlab工具进行应用实践。本文坚持以学生为中心，通过教学创新及应用实践的有限差分方法教学模式，为学生搭建理论与实践的纽带，激发学生的学习兴趣，增强学生解决问题的实践能力。
In the fields of computational science and engineering, numerical solution of differential equations has strong theoretical and practical significance. In this paper, we take the teaching of the finite difference method in the Numerical Solution of Differential Equations in the Information and Computing Science major as an example, explore the teaching innovation, derive five-point difference scheme from different senses and give the application practice using Matlab. This paper insists on taking students as the center to explore the teaching innovation and application practice for teaching model of finite difference method, and to build a link between the theory and practice for students, enhance students’ enthusiasm, and cultivate their ability to solve practical problems.