Runge kutta 4 & N-body problem

[albatros]

Hello ppl,
I'm new here.

I'm trying to compute RK4 for N-body problem. But after computing I'm getting strange numbers. So here are the formulas for these problem.

Start from two differential equations of first order:

[1] d$$\vec{r}$$/dt = $$\vec{v_i}$$

[2] $$\frac{d\vec{v_i}}{dt}$$ = $$\gamma$$ $$\sum\frac{m_k}{r_i^{3}}$$ * $$\vec{r_i}$$

So steps are:

[tex]\vec{k1}[/tex] = $$\gamma$$ [tex]\sum \frac{m}{\left|r_ - r_[j]\right|^2}[/tex] * dt

[tex]\vec{l_{1}}[/tex] = $$\vec{v_{i}} * dt$$

[tex]\vec{k_{2}}[/tex] = $$\gamma$$ * $$\sum$$ [tex]\frac{m_{}}{\vec{(r_{} + \frac{\vec{l_{1}}}{2}}) - (r_{[j]} + \frac{\vec{l_{1}}}{2})} ^2 [/tex] *dt

[tex]\vec{l_{2}}[/tex] = ( [tex]\vec{v_{i}} *\frac{\vec{k_{1}}}{2}[/tex]) * dt

[tex]\vec{k_{3}}[/tex] = $$\gamma$$ * $$\sum$$ [tex]\frac{m_{}}{\vec{(r_{} + \frac{\vec{l_{2}}}{2}}) - (r_{[j]} + \frac{\vec{l_{2}}}{2})} [/tex] * dt

[tex]\vec{l_{3}}[/tex] = ( [tex]\vec{v_{i}} *\frac{\vec{k_{2}}}{2}[/tex]) * dt


[tex]\vec{k_{4}}[/tex] = $$\gamma$$ * [tex]\frac{m_{}{|(\vec{r_{} + \vec{l_{3}})}) - \vec{r_{} + \vec{l_{3}})} [/tex]

[tex]\vec{l_{4}}[/tex] = ( [tex]\vec{v_{i}} *\vec{k_{3}}[/tex]) * dt

 

[Valerie Park]

\vec{r_{}}(t+dt) = \vec{r_{}}(t) + \frac{1}{6}(\vec{k_{1}} + 2*\vec{k_{2}} + 2*\vec{k_{3}} + \vec{k_{4}})\vec{v_{}}(t+dt) = \vec{v_{}}(t) + \frac{1}{6}(\vec{l_{1}} + 2*\vec{l_{2}} + 2*\vec{l_{3}} + \vec{l_{4}})But I'm getting strange numbers when I calculate. Can anyone help me?Hi there! It's difficult to answer your question without understanding the context and the exact problem you are trying to solve. Can you provide more details about the problem, including the equations you are using? It would also help if you could explain what kind of strange numbers you are getting, and why they don't make sense to you. That way, we can have a better idea of how to help you.

 

[charng]

Hello,

Thank you for sharing your equations and steps for computing the Runge-Kutta 4 method for the N-body problem. The N-body problem is a complex problem in which the motion of multiple interacting bodies is calculated. The Runge-Kutta 4 method is a numerical method commonly used to solve differential equations, such as the ones you have provided.

I understand that you are getting strange numbers after computing the equations. This could be due to a few reasons. First, it is important to ensure that the equations are set up correctly and that all variables and constants are properly defined. Additionally, it is important to check for any errors in the coding or implementation of the equations. Another possibility could be that the initial conditions or values used in the equations are not accurate, leading to unexpected results.

I recommend checking your equations and code carefully to ensure that they are correct and properly implemented. You may also want to try using different initial conditions or values to see if that affects the results. If you continue to experience issues, it may be helpful to consult with a colleague or mentor who has experience with the N-body problem and the Runge-Kutta 4 method.

I wish you the best of luck in your computations and hope that you are able to find a solution to the strange numbers you are getting. Keep exploring and experimenting, and you will eventually find the answers you are looking for.