Numerically Solve Differential Equations in MATLAB | #ode45 examples

Welcome to Laplace Academy
Today we are going to learn about solving differential equations numerically in MATLAB.

In my previous tutorial I discussed how to solve ODEs analytically, using dsolve command in MATLAB.

But most of the times, our differential equations do not have an analytical solution. So, we must try numerical functions such as ode45.

Ode45 is a powerful initial value problem solver in MATLAB. It is important for any MATLAB user, to learn how to make the most out of this command. In this tutorial I discuss how to use it to solve differential equations.

🔻🔻🔻🔻🔻🔻🔻🔻🔻🔻🔻🔻🔻🔻🔻🔻
Links To Other Tutorials, which might be of help to you:

To solve differential equations analytically:

To define functions in MATLAB:

If you want to solve any equation in MATLAB:

If you want to know more about symbolic tools in MATLAB:

If you want to learn 2d Plotting in MATLAB:

What do you want my next tutorial to be? 😉 Leave me a comment..

♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦
This video is the first part of Differential Equations in MATLAB.
To see the full playlist:

Please consider hitting the SUBSCRIBE button. Or click on the link below:

If you want to learn MATLAB:

You can also follow me on
Instagram:

Facebook:

LinkedIn:

Twitter:

0:00 - Intro
0:35 - Example of Using ode45
3:04 - Solving a system of differential equations in MATLAB
4:57 - Solving a second order ODE in MATLAB using ode45
6:33 - Solving a system of two second order differential equation using ode45
8:44 - One more example to practice using ode45

#matlab #ode45

[akash_mechanical]

#.Very systematic, good for begineers and revising ODE 45. Thanks for it..🤗

Great video, I have a Numerical Methods exam on monday. Came here to help me better understand some parts.

[vking]

This is a really helpful video. I tried rewriting keplers equations in 3 dimensions, which i thought would be an easy extension from what you did – 3 2nd order ODE's means 6 1st order ODE's with 6 initial conditions – but it was not easy. Why don't you consider the gravitational parameter, mu, in your example for keplers equation? I find when i add mu to your code, then the graph falls apart.

[dj-play]

Decent video. For improvement I recommend taking a little longer to break down writing the 2 first order equations as a 2nd order equation further.

[tamannaahuja]

Thanks for the video but in my matlab it’s showing “execution of script ODEE45 as. a function is not supported.
Please help

[hammaminadjima]

Hello. Thanks for the nice video. I would like to know how can we solve a boundary value problem. I mean if the initial condition is at the non-zero value of an independent variable.

[Vlad.]

last initial condition for Kepler equations that you provided is sqrt of a negative number so how does it work?

[AjayKumar-uldg]

it is showing Unrecognized function or variable 't' in my case.

[aajamerepyar]

how to plot y' vs y and y' vs x in the ode45

[yzhofxj]

yeah nice video, but how do i get the actual equation for u and v? isn't that as well the actual solution of the differential equation?