Julia语言是一门灵活的免费开源的动态编程语言，具有编译型语言和解释型语言的优点，适用于科学计算和数值分析。学习和掌握Julia语言，可以帮助人们进行物理问题的深入分析和研究。
本论文比较详细地介绍了关于求解经典力学二阶微分方程的数值方法Euler法和Runge-Kutta法，和求解量子力学定态薛定谔方程的数值方法Numerov法的理论原理，并使用Julia语言实现Euler法、Runge-Kutta法和Numerov法的算法。其中，还将上述算法用于具体物理问题中解决问题，在经典力学中解决一维谐振子问题时，比较了Euler法、二阶Runge-Kutta法和四阶Runge-Kutta法的优劣，并使用了四阶Runge-Kutta法解决二维经典谐振子问题；在量子力学中，使用Numerov法解决一维和二维谐振子问题。另外，还使用Plots工具包将物体的运动状态可视化，帮助人们更好地研究物理的运动过程。
本研究的实践结果表明，当使用上述的算法代码去解决具体问题时，发现得到的数值计算解与理论值数据比较吻合，说明算法代码具有一定的可行性。同时发现，数值解与理论值之间存在一定的误差，而这些算法的适用也存在一定的局限性，所以其算法还需要进一步完善。

Julia language is a flexible, free and open source dynamic programming language with the advantages of both compiled and interpreted languages, suitable for scientific computing and numerical analysis.Learning and mastering Julia language can help people conduct in-depth analysis and research on physical problems.
This paper introduces in detail the Euler method and Runge-Kutta method for solving the second order differential equation of classical mechanics, and the Numerov method for solving the fixed state Schrodinger equation of quantum mechanics.The Euler method, Runge-Kutta method and Numerov method are coded by Julia language.And the above algorithms are also used to solve specific physical problems.When solving one-dimensional harmonic oscillator problems in classical mechanics, the advantages and disadvantages of Euler method, second-order Runge-Kutta method and fourth-order Runge-Kutta method are compared, and the fourth-order Runge-Kutta method is used to solve two-dimensional classical harmonic oscillator problems.The Numerov method is used to solve one - and two-dimensional harmonic oscillator problems in quantum mechanics.The Plots kit will also be used to visualize the motion of objects ,to help people better study the physical process.
The practical results of this study show that when the algorithm code mentioned above is used to solve specific problems, it is found that the numerical calculation solution is quite consistent with the theoretical data, indicating that the algorithm code has certain feasibility.At the same time, it is found that there is some error between the numerical solution and the theoretical value, and the applicability of these algorithms also has some limitations, so the algorithm needs to be further improved.