高阶线性常微分方程显式Euler法的数值分析

Numerical Analysis of High-Order Linear Ordinary Differential Equations via Explicit Euler Method

摘要: 针对高阶线性常微分方程，建立了显式Euler格式，分析了数值格式的局部截断误差，并在舍入误差条件下，获得了数值解的全局误差，同时，讨论了数值解的渐进稳定性。常系数与变系数二阶算例验证了理论分析结果的正确性与有效性。

Abstract: An explicit Euler scheme is established for high-order linear ordinary differential equations. The local truncation error of the numerical scheme is analyzed. Under the condition of rounding errors, the global error of the numerical solution is obtained. Also, the asymptotic stability of the numerical solution is discussed. The theoretical analysis results are verified to be correct and effective through constant-coefficient and variable-coefficient second-order ordinary differential equations.