基于欧拉方法求解微分方程初值问题

Solving Initial Value Problems of Differential Equations Based on Euler Method

摘要: 微分方程在数学实际应用以及物理、化学、生物等众多领域中被应用得十分广泛。欧拉法是求解微分方程最基本、最常用的方法，而改进欧拉法则是在欧拉法的基础上进行相应的改进而形成的方法。本文对比关于欧拉法的三种方法近似解与精确解的关系，并根据其具体计算结果进行对比，得到改进欧拉法的计算效率更高、精度更高。

Abstract: Differential equations are widely used in many fields such as mathematics, physics, chemistry, bi-ology and so on. Euler method is the most basic and commonly used method to solve differential equation, and the improved Euler method is a method based on the corresponding improvement of Euler method. In this paper, the relationship between the approximate solution and the exact solution of the three Euler methods is compared, and according to the specific calculation results, the improved Euler method is more efficient and more accurate.