Solving Coupled ODEs with 4th Order Runge-Kutta Method

[Dr. G]

Can a 4th order Runge-Kutta method be used to solve an equation of this form:

dVx/dt = ωVy , where ω = constant. and Vx and Vy are the x and y components of the velocity.

 

[DrClaude]

That's not much of an equation to solve, as the right-hand-side is constant. You would need an equation for V_y also.

 

[Dr. G]

That's not much of an equation to solve, as the right-hand-side is constant. You would need an equation for V_y also.

The equation for Vy is
dVy/dt = - ω Vx. And I have the I.C's. So, I can uncouple them. But if the magnetic field is more complicated, hence making ω more complicated, then I would like to see if I could use an
RK4 method to solve them. (These equations arise from the Lorentz force equation.)

 

[DrClaude]

Yes, RK is then a good choice.