Solving Ordinary Differential Equations with MATLAB

Learn the basics of solving ordinary differential equations in MATLAB®. Use MATLAB® ODE solvers to find solutions to ordinary differential equations that describe phenomena ranging from population dynamics to the evolution of the universe.

Course modules

Introduction

Familiarize yourself with ordinary differential equations and the course.

Lessons:
  • Course Overview

What is an Ordinary Differential Equation?

Introduce ordinary differential equations and their solutions.

Lessons:
  • Course Example - The Shuttle Launch
  • Introducing the Differential Equation
  • Solutions to Differential Equations

Solving ODEs Numerically

Solve first order ODEs numerically using the ode45 function.

Lessons:
  • Using MATLAB ODE Solvers
  • Writing ODE Functions
  • Obtaining a General Solution Structure
  • Review - Solving ODEs Numerically

Solving Systems of ODEs Numerically

Solve systems of first order ODEs numerically.

Lessons:
  • Course Example - The SIR Model
  • Implementing a First-Order System of ODEs
  • Using ode45 to Solve Systems of ODEs
  • Review - Solving Systems of ODEs Numerically

Solving Higher-Order ODEs Numerically

Solve higher-order ODEs numerically.

Lessons:
  • Identifying Higher-Order ODEs
  • Writing Higher-Order ODEs as First-Order Systems
  • Solving Higher-Order ODEs with ode45
  • Review - Solving Higher-Order ODEs Numerically

Next Steps

Give feedback on the course.

Lessons:
  • Additional Resources
  • Survey

MATLAB Onramp

Get started quickly with the basics of MATLAB.

Simulink Onramp

Get started quickly with the basics of Simulink.

MATLAB Fundamentals

Learn core MATLAB functionality for data analysis, modeling, and programming.

MATLAB Onramp

Get started quickly with the basics of MATLAB.