Solving Differential Equations
In this section, I will describe methods for solving differential equations, specifically focusing on Simpson’s One-Third Rule and the Runge-Kutta Methods (Second Order and Fourth Order).
What is a Differential Equation?
A differential equation is an equation that relates a function with its derivatives. Differential equations describe various phenomena such as heat, motion, electricity, and fluid flow. The solution to a differential equation is a function that satisfies the equation.
Example
Consider the first-order differential equation:
[ \frac{dy}{dx} = x + y ]
To solve this equation, we need to find the function ( y(x) ) that satisfies this relationship.
Next, we will delve into the detailed implementation of these methods.