常微分方程数值解法的教学探索

The Teaching Exploration of Numerical Methods for Ordinary Differential Equations

摘要: 针对数值分析课程中的常微分方程数值解法，本文提出了一种结合计算机辅助工具和问题导向学习(PBL)的教学改革方案，以Lotka-Volterra捕食–被捕食模型为例，通过四阶龙格–库塔法求解常微分方程，强化学生的理论理解与应用能力。目标是通过该教学探索，提高了学生的数值计算能力和问题解决能力。

Abstract: For the numerical analysis course focusing on numerical methods for solving ordinary differential equations (ODEs), this paper proposes a teaching reform plan that integrates computer-assisted tools with problem-based learning (PBL). Using the Lotka-Volterra predator-prey model as an example, the fourth-order Runge-Kutta method is employed to solve ordinary differential equations, aiming to enhance students’ theoretical understanding and practical application skills. The goal of this teaching approach is to improve students’ numerical computation capabilities and problem-solving abilities.