Questions tagged [runge-kutta]
The Runge–Kutta methods are a set of numerical methods for ordinary differential equations for the approximation of their solutions.
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Which Runge-Kutta method is more accurate: Dormand-Prince or Cash-Karp?
I simply want to know whether the Dormand-Prince Numerical Method
or the Cash-Karp Numerical Method
is more accurate.
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Easily understandable argument that normal Runge–Kutta methods cannot be generalised to SDEs?
A naïve approach to solving stochastic differential equations (SDEs) would be:
take a regular multi-step Runge–Kutta method,
use a sufficiently fine discretisation of the underlying Wiener process,
...
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Fourth order IMEX Runge-Kutta method
I am looking for the Butcher tableau of a fourth order accurate Runge-Kutta method with IMEX splitting. I have been reading the ''classical'' paper on the subject by Ascher, Ruuth and Spiteri as well ...
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4th order Runge-Kutta Method for Driven Damped Pendulum
Although I've been looking everywhere, I have been unable to find an answer to my question so here it is. For a driven damped pendulum the equation of motion in dimensionless units is,
$$\alpha(\...
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How can I call the Boost C++ odeint Runge-Kutta integrator for a system of ODEs?
I would like to use Boost C++ odeint Runge-Kutta integrator on a system that looks like this :
$$\ddot x = - \frac A{||x||^3} * x $$
$ x $ is a vector in 3D space, so basicaly $ x(i, j, k) $
$ \...
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BDF vs implicit Runge Kutta time stepping
Are there any reasons for why one should choose high order implicit Runge Kutta (IMRK) over BDF time stepping? BDF seems much easier to me as $q$ stage IMRK needs $q$ linear solves per time step. ...
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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 ...
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Applying the Runge-Kutta method to second order ODEs
How can I replace the Euler method by Runge-Kutta 4th order to determine the free fall motion in not constant gravitional magnitude (eg. free fall from 10 000 km above ground)?
So far I wrote simple ...
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Is there any explicit symplectic Runge-Kutta method?
As far as I know, all the symplectic Runge-Kutta methods are implicit which need to solve non-linear equations during the calculation. Is there any explicit method? If not, why?
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Intermediate values (interpolation) after Runge-Kutta calculation
I have a numerical ODE simulation that I computed at fixed time step $h$ using a 4-th order Runge-Kutta method (RK4), producing a series of results $(x_1,y_1), (x_2,...
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How to estimate the local error and the global error for Runge-Kutta method
How to estimate the local error and the global error for Runge-Kutta method used for solve a system of differential equations in practice?
I use Richardson extrapolation for select a adaptive step [...
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4th-order Runge-Kutta method for coupled harmonic oscillator
I’m attempting to write a C program to gather values from a coupled spring system: There is a wall, connected to a mass $m_1$ by a spring, then this mass is connected to a second mass $m_2$ by another ...
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Runge Kutta and Milstein – system of second-order coupled differential equations with noise
I would like to solve a system of second-order differential equations to describe the dynamics of a system of particles.
Two Newton-like forces are responsible for the motion of each particle $i$: A ...
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Integration of differential equation with orthogonality constraint
Lets say I have a system of differential equations which has the form
$$\dot{C}_{\alpha,\beta,m} = f_{\alpha,\beta,m}(C_{\alpha,\beta,1},\ldots,C_{\alpha,\beta,N};t).$$
The $f$s are some functions of ...
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Determine numerical infinity for Schrodinger equation $−\psi''(x) + x^ 2 \psi(x) = E\psi(x)$
Consider the following Schrodinger equation for the harmonic oscillator with real $x$:
$$
−ψ''(x) + x^ 2 ψ(x) = Eψ(x).
$$
I solve the last equation using shooting method and implicit Runge-Kutta ...
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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
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Implementation details for high order IMEX methods by Kennedy and Carpenter
This question is a continuation of
Fourth order IMEX Runge-Kutta method, concerning the implementation. Is seems to me that the first implicit stage value involves a direct evaluation, rather than ...
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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 ...
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Confirmation of FSAL property for IMEX methods by Kennedy and Carpenter
This question is a continuation of
Fourth order IMEX Runge-Kutta method and Implementation details for high order IMEX methods by Kennedy and Carpenter.
I need confirmation that ARK3(2)4L[2]SA by ...
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