In this chapter we study numerical methods for solving a first order differential equation
\[
y'=f(x,y).
\]
SECTION 3.1 deals with Euler’s method, which is really too crude to be of much use in practical applications. However, its simplicity allows for an introduction to the ideas required to understand the better methods discussed in the other two sections.
SECTION 3.2 discusses improvements on Euler’s method.
SECTION 3.3 deals with the Runge-Kutta method, perhaps the most widely used method for numerical solution of differential equations.
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