Solving the Blasius Solution Using the Runge-Kutta Method

This paper explores the application of the Runge-Kutta method as an effective tool for solving higher-order differential equations. To facilitate deeper understanding, we thoroughly discuss the mathematical principles underlying the Runge-Kutta algorithm, including its iterative calculation process and error control mechanisms. The implementation demonstrates how to code this method in MATLAB, highlighting critical functions like ode45 for adaptive step-size control and explaining algorithm customization for boundary value problems. Practical examples are provided to illustrate the method's application in solving the Blasius equation, with code annotations detailing variable initialization, derivative function handling, and results visualization. Through comprehensive theoretical explanations and practical coding demonstrations, this paper aims to equip readers with solid understanding of Runge-Kutta implementation for complex differential equations.