3: Numerical Methods — Read — Invisible Network

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In this chapter we study numerical methods for solving a ﬁrst order differential equation \(y' = f(x,y) \nonumber\).

3.1: Euler's Method
This section 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.
- 3.1.1: Euler’s Method (Exercises)
3.2: The Improved Euler Method and Related Methods
Euler’s method implies that we can achieve arbitrarily accurate results with Euler’s method by simply choosing the step size sufficiently small. However, this isn’t a good idea, for two reasons. (1) After a certain point decreasing the step size will increase roundoff errors to the point where the accuracy will deteriorate rather than improve. (2)The expensive part of the computation is the evaluation of the solution. This section discusses improvements on Euler’s method.
- 3.2.1: The Improved Euler Method and Related Methods (Exercises)
3.3: The Runge-Kutta Method
This section deals with the Runge-Kutta method, perhaps the most widely used method for numerical solution of differential equations.
- 3.3.1: The Runge-Kutta Method (Exercises)

This page titled 3: Numerical Methods was last modified on Tue, 07 Jan 2020 03:43:41 GMT and is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by William F. Trench.

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