Part VI Numerical Methods
Numerical methods are a collection of techniques used to approximate solutions to mathematical problems that cannot be solved analytically. In this chapter, we will learn about some of the most common numerical methods used to solve differential equations.
We will start by discussing Euler’s method, a simple numerical technique for solving first-order ordinary differential equations. We will then move on to more advanced methods such as Runge-Kutta methods, which are used to solve higher-order differential equations and systems of differential equations.
We will also learn about error analysis and how to estimate the accuracy of numerical solutions. Understanding the limitations of numerical methods is crucial for obtaining reliable results.
We will work through several examples to illustrate the application of numerical methods. By the end of this chapter, you should be able to apply these techniques to solve a wide range of differential equations numerically.
Let’s get started!
