Practical MATLAB Modeling with Simulink: Programming and Simulating Ordinary and Partial Differential Equations

© Sulaymon L. Eshkabilov 2020

S. L. EshkabilovPractical MATLAB Modeling with Simulinkhttps://doi.org/10.1007/978-1-4842-5799-9_2

2. Numerical Methods for First-Order ODEs

Sulaymon L. Eshkabilov¹ 

(1)

Ag & Biosystems Engineering Department, North Dakota State University, Fargo, USA

 

This chapter is dedicated to using numerical methods to solve initial-value problems (IVPs) of ODEs. The methods we’ll use are Euler, Runge-Kutta, Adams, Taylor, Milne, and Adams-Moulton. Specifically, we will evaluate their accuracy and efficiency. Of these methods, the Euler method is the simplest one and actually has several types, such as forward, backward, and improved (modified).

Euler Method

As mentioned, there are three different types of Euler methods to compute numerical ...