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# Chapter 23. Ordinary Differential Equation - Boundary Value Problems¶

## Motivation¶

After the discussion of ODE initial value problems, in this chapter, we will introduce another type of problems - the boundary value problems.

The boundary value problem in ODE is an ordinary differential equation together with a set of additional constraints, that is boundary conditions. There are many boundary value problems in science and engineering. Therefore, this chapter covers the basics of ordinary differential equations with specified boundary values. We will discuss two methods for solving boundary value problems, the shooting methods and finite difference methods. By the end of this chapter, you should understand what ordinary differential equation boundary value problems are, how to pose these problems to Python, and how to solve the problems.