How to code second order differential equation with input variable t?
1 view (last 30 days)
Show older comments
Saruultugs Batzorig
on 6 Nov 2019
Commented: Saruultugs Batzorig
on 6 Nov 2019
Hello, how do I implement the following second order differential equation with input variable t (0 to 300) and output the corresponding displacement h? Thank you.
1369.8*h + 2566.7*hdot + 2.785e7*hdotdot - 2091.2*exp(-0.59452*t)*(exp(0.59452*t) + 1.0) = 0
0 Comments
Accepted Answer
Mark Rzewnicki
on 6 Nov 2019
Edited: Mark Rzewnicki
on 6 Nov 2019
Looks like we have a 2nd-order differential equation of function . To clean the problem up, let's define some constants:
, , , ,
Then we have the following expression:
Now get by itself so we can use a numerical method to integrate the system:
Suppose you define . Then the system is determined for when you specify the initial conditions: .
Notice that .
Let a very small change in t be denoted . Then you could approximate the value of using the relation .
So the process looks like this:
1. Start at and specify the initial conditions and . This allows you to calculate .
2. Use and to determine and h after a tiny step . Now you can calculate .
3. Use and to determine and h after another tiny step . Update the value of .
4. Repeat until .
This process is called "rectangular integration" and it allows you to numerically solve DEs quickly. If you want higher accuracy, you can use a Runge-Kutta method. These methods follow a very similar procedure but reduce the estimation error at every step. A popular one is a fourth-order method commonly called "RK4."
EDIT: I played around simplifying the original equations. Notice that .
More Answers (0)
See Also
Categories
Find more on Ordinary Differential Equations in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!