# 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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### Runge-Kutta methods, higher derivative methods, and collocation methods

Consider an ODE system $$\dot x = f(t, x), \quad x(0) = \xi.$$ A collocation method to solve this ODE (1) assumes that $x$ can be approximated as a polynomial $x(t) \approx \sum_kx_kp_k(t)$ and (2) ...
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### Estimating the spectral radius when applying the method of lines

Some time integrators, notably the Runge-Kutta-Chebyshev method, implemented in the RKC code from Sommeijer & Verwer, gives the user an option to provide a callback with an estimate of the ...
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### Solving 1D Advection Equation Using Midpoint-Rule and Finite-Differences

I want to solve the advection equation ($v_0 \in \mathbb R$) $$\frac{\partial f}{\partial t} + v_0 \frac{\partial f}{\partial x} = 0$$ using 2nd order Runge Kutta like the midpoint rule for the time ...
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### RK4-method starts oscillating above certain input parameters

I am trying to solve an equation of the following type $$\partial_zE(z)=-c_0J$$ with $$J=c_1\beta E^3(z)$$ using the boost::odeint-framework and a fixed time stepper, with $c_0$, $c_1$ and $\beta$ ...
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### Shooting Method with RK4 and Thermal Radiation

I am attempting to numerically solve the following problem. I decompose it into a system of two first order ODEs and then solve via the shooting method. I use the fourth order Runge-Kutta (RK4) method ...
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### Numerically solving a partial differential equation in python with Runge Kutta 4

I'm supposed to solve the following partial differential equation in python using Runge-Kutta 4 method in time. $$\frac{\partial}{\partial t}v(y,t)=Lv(t,y)$$ where $L$ is the following linear ...
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### Runge-Kutta for PID and system in separate calculations without filter

I need to calculate a closed-loop system in Python; specifically, obtain the PID response and then use the output to obtain the system response sample-by-sample with my own loop. For this, I am ...
1 vote
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### Successive iteration method for solving eigenvalue ploblem

I have a question concerning the branch of successive iteration methods (Newton, Runge-Kutta). I definitely know (or can read in Wikipedia) the implementation of these methods. But I was wondering ...
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### How and when to use IMEX runge-kutta

i have come across method of IMEX Runge-Kutta written by Kennedy and Carpenter in july 2001. The method consist of two kind that is "implicit and explicit" can i use the ERK@explicit part only to ...
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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 ...
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### Computing solutions with singularities using MATLAB ODE45

I am new to solving numerically ODES and thus it is difficult for me to judge the reliability/trustworthiness of the results that I have produced for the following problem: I am dealing with a 2nd ...
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One beginner's question about discretization of a Hamilton-Jacobi equation(non-linear) $$u_t = H(u_x)$$ $u_x$ is discreated with 2nd order ENO-FD 1st order: $D_1^{\pm}u = \pm [u_{x\pm1} - u_x ] / \... 0 votes 0 answers 2k views ### 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 0 votes 0 answers 96 views ### Computing Trajectory Equations of Kerr Geodesics I want to numerically solve the trajectory equations of a Kerr geodesic given by wikipedia in Matlab. The trajectories look like: I implemented the equations and solved it with the standard Runge-... 0 votes 0 answers 499 views ### Finding second excited state of Schrödinger equation with secant Runge Kutta method In our assignment, we are required to find the energies of the ground state and the first two excited states of the Schrödinger equation in a harmonic potential:$$V = \frac{50 x^2}{(10^{-11})^2}\, .$...
I am applying a 4th order Runge-Kutta code, using the method of lines, to solve the following: $$\frac {\partial y_1}{\partial t} = y_2 y_3 - C_1 y_1$$ \...