All Questions
Tagged with computational-physics runge-kutta
14
questions
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Solving perturbed Einstein Boltzmann equations using RK4
I'm trying to learn to numerically solve the perturbed Boltzmann-Einstein equations in cosmology using the RK4 method.
These are the equations:
$$\dot{\Theta}_{r,0}+k\Theta_{r,1}=-\dot{\Phi}$$
$$\dot{\...
- 23
1
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1
answer
584
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RK4 integration of the three-bodies problem with C++
first of all thank you for all the answers you gave me yesterday for the integration via Symplectic Euler's method of the three-body problem.
We managed to implement both Euler's and Runge Kutta 4's ...
- 171
2
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1
answer
1k
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N-body problem with differents solvers (RK2, RK4, Euler symplectic, Stormer-Verlet) : planets drift to infinity
I'm trying to write an integrator for the 2 and 3-body problem. I choose to start from a generalisation to N-body problem so I can just pass my bodies to the same integrator in the two cases.
I'm ...
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0
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Solving nonlinear pendulum using Runge-Kutta 4 for smaller steps
I am trying to solve nonlinear pendulum using 4th order Runge-Kutta method for limits between a=0.0 to b=110 seconds and simulated the results to observe the pendulum movement. But when I increase the ...
- 276
2
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1
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915
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Runge-Kutta fourth order method. Integrating backwards
I am using a Runge-Kutta fourth order method to solve numerically the usual equation of motion of a background scalar field in curved spacetime with a quartic potential:
$\phi^{''}=-3\left(1+\frac{H^{...
user33042
2
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1
answer
603
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Langevin equation in 4th order Runge-Kutta
I'm trying to figure out how to translate a piece of code from Velocity Verlet to Runge-Kutta, while treating the time step dependence of the thermal noise correctly.
The Langevin equation for my ...
- 23
1
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1
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467
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How to obtain and form a 1st order differential equation for leapfrog integration from second order one in this example of coulomb drag
I am currently doing a computational physics homework which asked us to use leapfrog to give the relations between timevelocities and time-distance of these two objects.
The full question is as ...
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5
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1
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How can I apply Euler's Method to predict a point in time rotating around multiple axis'
I am xposting this from my original stackoverflow question where I was presented with a coding challenge that I have been able to narrow down extensively and I think it lies with Euler's Method.
Here'...
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1
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0
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3k
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Using RK2 Method to solve the simple harmonic oscillator of a horizontal mass on a spring (1D)
Being new to numerical analysis techniques, in particular RK2, I decided the best way to jump in is by using python to solve the well known mass-spring oscillator using RK2 techniques.
My problem is ...
- 111
1
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1
answer
625
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Higher-order Verlet integration
I'm using a simple version of Verlet integration for a particle–particle interaction system with collisions. At the end of each iteration, I integrate like this:
...
2
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1
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Can 3rd order TVD admit perfect shift for Upwind 1D Advection equation?
I recently coded a 1 stage and 3 stage optimal TVD-RK explicit scheme using eqn 3.3 here
http://www.ams.org/journals/mcom/1998-67-221/S0025-5718-98-00913-2/
on the equation Ux+Uy=0, where x and y ...
- 149
1
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1
answer
434
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Numerical Free Fall Analysis with RK4
I am trying to calculate real speed and time in free fall of a body. I wrote a code in Fortran and I am trying to improve it by using RK4 method
x=time y=total free fall
Purple line using:
...
- 113
16
votes
1
answer
3k
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Why is leapfrog integration symplectic and RK4 not, if the latter is more accurate?
In a system where energy theoretically should be conserved, the most accurate simulation would conserve energy (as well as giving accurate positions, velocities and etc). RK4 is more accurate than ...
- 275
2
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1
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1k
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Object falling with air resistance using Runge-Kutta
I am not very familiar with differential equations, nor physics in general. I am trying to program an object falling with air resistance with the use of a numerical algorithm called Runge-Kutta. The ...
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