Numerically Solve Differential Equations in MATLAB |

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.
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Links To Other Tutorials, which might be of help to you:
To solve differential equations analytically:
• Solve Differential Equ...
To define functions in MATLAB:
• Define Functions in MA...
If you want to solve any equation in MATLAB:
• Learn to Solve Any Equ...
If you want to know more about symbolic tools in MATLAB:
• MATLAB Symbolic Toolbo...
If you want to learn 2d Plotting in MATLAB:
• 2D Plotting in MATLAB ...
What do you want my next tutorial to be? 😉 Leave me a comment..
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This video is the first part of Differential Equations in MATLAB.
To see the full playlist:
• Differential Equations...
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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

[@sarah-tq5qh]

Keep going ⭐

[@vking4983]

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.

[@mohamed__sherif]

Great Video

[@LaplaceAcademy]

Thanks!

[@nauleshkumar8703]

short and handy videos, thanks

[@LaplaceAcademy]

You're welcome. I'm glad you liked it

[@PymGordonArthur]

Thanks for the upload.

[@LaplaceAcademy]

I'm glad I could help you 🏌️

[@arpangarg6112]

Excellent

[@LaplaceAcademy]

I am glad that I could help you.

[@fabjulian7926]

insane, thank you so much!

[@LaplaceAcademy]

You're welcome

[@hammaminadjima3813]

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.

[@LaplaceAcademy]

Hi. Thanks for your comment. Here's the link to another tutorial. I hope it helps you. kzbin.info/www/bejne/Zl6ZfXx6asyNnrM

[@pawejerzyna5674]

this video was put simply, thanks

[@LaplaceAcademy]

You're welcome.

[@tamannaahuja8640]

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

[@aajamerepyar4586]

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

[@mathematics__07]

Sir please tell about cauchy problem

[@Vlad.007]

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

[@LaplaceAcademy]

The variable 'e' is always smaller than 1. So the initial condition is not going to be sqrt of a negative value.

[@user-yz6ho8fx8j]

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?

[@LaplaceAcademy]

Not every differential equation has an analytical answer. But you can always try. Learn how to use dsolve command for the exact solution of ODEs. Here's the link: kzbin.info/www/bejne/opqxaHZve9hsm9k

[@faridnajafzadehasl6315]

Perfect

[@LaplaceAcademy]

Thanks mate

[@HadiB-mo4wy]

Nice accent ❤

[@LaplaceAcademy]

Love you mate ❤️👽🍒