Runge-Kutta method related

Hi

   I have a doubt (rather a confusion) in Ruge-Kutta method. I want to time integrate an equation of the form

                 dy/dt = g*n-0.5*(u^2+v^2)

Where g,n,u and v are known. So I can put equation in the form

                  dy/dt = a constant

I want to time integrate it in the time span [ti tf]. As the equation have constant on right side and no time, no y variable, how I can time integrate it? I have initial conditions for y. If I use ode45 how I can call ode45? How the equation should be fed to ode45?

Thanks in advance

Sreenu

Answer 1

[Richard Brown]

Why are you bothering to use ode45 at all?

Your solution for any t >= ti is just

y = y0 + (t - ti) * (g*n-0.5*(u^2+v^2));

[Jan]

Phew, you revealed the secret. ;-)

[Richard Brown]

"You can integrate the function dy/dt=K in closed form also.", Sorry, didn't see this bit in your answer!

[KSSV]

Dear Richard

Perfect. Yes, we can solve the equation by using first order difference;

y = y0 + dt*(g*n-0.5*(U^2+v^2))

This what I have followed. The author says, RK4 will be of less error compared to first order difference. So, no option at last I have to integrate using RK4.

[Jan]

No doubt, Richard, you hit the point: The integration of a constant is trivial. +1

Answer 2

[Jan]

Did you read the documentation for ODE already? There is a nice example, which you can modify easily.

[KSSV]

I used ODE45 n number of times, I know how to invoke/call ODE45. I already mentioned that my equation happens to be of the form

dy/dt = K

I am confused of the methodology to be applied in this case. I tried ODE45 for the equation, but the results are not satisfactory.

[Jan]

Please post how you have implemented the function to be integrated and explain "not satisfying" with any details. The solution seems to be trivial: function dy=myFunc(y, t) dy = 15.3; % Or what ever the constant value is

You can integrate the function dy/dt=K in closed form also.

Perhaps you are looking for an anonymous function to define the constant value externally. Then see: http://www.mathworks.com/matlabcentral/answers/1971-when-using-ode45-or-similar-functions-what-is-the-benefit-of-using-anonymous-functions-over-passi Another idea is to search for the term "ODE45" in this forum.