基于Newton迭代动态调整的Runge-Kutta法的构造及其在Blasius方程中的应用
Construction of the Runge-Kutta Method Based on Newton’s Iterative Dynamic Adjustment and Its Application to the Blasius Equation

本文提出了一种新型数值求解方法，该方法将四阶Runge-Kutta法与Newton迭代法相结合，旨在高效求解流体力学中的Blasius方程边值问题。首先，我们将Blasius方程转化为一组一阶微分方程组，并采用四阶Runge-Kutta法(RK4)进行数值求解。随后，引入Newton迭代法动态调整初始条件，以确保满足边界条件的要求。实验结果表明，与传统的打靶法和结合打靶法的四阶Runge-Kutta法(SRK)进行对比实验，新方法在迭代次数和计算时间上均展现显著优势，同时求解精度也得到提升。
In this paper, we propose a novel numerical solution method that combines the fourth-order Runge-Kutta method with the Newton iterative method, aiming to efficiently solve the margin problem of Blasius equation in fluid mechanics. Firstly, we transform the Blasius equation into a set of first-order differential equations and solve it numerically using the fourth-order Runge-Kutta method (RK4). Subsequently, the Newton iteration method is dynamically introduced to adjust the initial conditions to ensure that the boundary conditions are satisfied. The experimental results show that the new method exhibits significant advantages in terms of the number of iterations and computation time, as well as improved solution accuracy, in comparison experiments with the traditional shooting method and the Runge-Kutta method (SRK) combined with the improved shooting method.