Coupled first order differential equations

How i can solve a system of 6 first order differential equations by using numerical techniques like Euler method, RK-4th order method , ODE -45 etc.
 
First you need to write the equations in state vairable form and then convert it to state space format where
xdot = Ax + B A is a matrix, x and B are vectors
y = Cx + Du C is the relationship between x and y, and D is an initial condition

Now just pick a single equation and perform your numerical calculations plug those results into all the others and see what you obtain, doing this by hand really isn't recommended. It far worse than solving a system of 6 ordinary algebraic equations by hand whihc is already quite the task. I suggest running ODE 45 on it in matlab
 

saltydog

Science Advisor
Homework Helper
1,582
2
Rafique Mir said:
How i can solve a system of 6 first order differential equations by using numerical techniques like Euler method, RK-4th order method , ODE -45 etc.
Here you go dude:

[tex]\frac{dx_1}{dt}=f_1(t,x_1,x_2,x_3,x_4,x_5,x_6)[/tex]
[tex].[/tex]

[tex].[/tex]

[tex].[/tex]

[tex]\frac{dx_6}{dt}=f_6(t,x_1,x_2,x_3,x_4,x_5,x_6)[/tex]

Now, each time you increment t, you have to determine the corresponding increments in [itex]x_i[/itex].

You see, it's done in parallel: Increment t, calculate [itex]x_1[/tex] through [itex]x_6[/itex] increment, then increment t again, do all six again, and so fourth to the end.

How about posting the equations?
 
Last edited:

Related Threads for: Coupled first order differential equations

Replies
5
Views
11K
Replies
1
Views
2K
Replies
11
Views
38K
  • Posted
Replies
4
Views
2K
Replies
11
Views
947
Replies
4
Views
733
Replies
2
Views
2K
  • Posted
Replies
2
Views
2K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads

Top