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_5

5. Higher-Order and Coupled ODEs

Sulaymon L. Eshkabilov¹ 

(1)

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

 

This chapter is dedicated to solving higher-order and coupled ODEs numerically. In general, the procedures used to solve higher-order ODEs and coupled systems of ODEs are similar to the ones used for second-order ODEs except for the additional steps required for new variables while rewriting the given higher-order ODEs as a system of first-order ODEs.

Fourth-Order ODE Problem

Let’s consider the following fourth-order nonhomogeneous ODE:

, y(0) = 50, dy(0) = 40, d²y(0) = 30, d³y(0) = 20. ...