In this paper, one-dimensional Burgers equation and one-dimensional Laval nozzle flow Euler equation are numerically solved, and the stability of the numerical solutions is analyzed theoretically. In order to satisfy the stability of the numerical solution, the explicit MacCormack scheme is used to obtain the stable solution of the computer numerical simulation. In addition, the numerical and analytical solutions of the Euler equation for one-dimensional Laval nozzle flow are compared, and the results are completely consistent, which verifies the correctness of the numerical solution.

中文翻译：

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一类非线性微分方程的数值解和稳定性分析

本文对一维Burgers方程和一维Laval喷嘴流量Euler方程进行了数值求解，并对数值解的稳定性进行了理论分析。为了满足数值解的稳定性，采用显式MacCormack方案获得计算机数值模拟的稳定解。另外，比较了一维拉瓦尔喷嘴流量的欧拉方程的数值和解析解，结果是完全一致的，验证了数值解的正确性。