# 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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### solving coupled ODEs using runge kutta method

I want to solve the following sets of n coupled equations. Initial values of x[n] and p[n] are specified. The problem is, I have an 1D lattice where every particle is bound with neighbouring ...
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### Type of Rosenbrock method by its coefficients

A Fortran code that solves stiff PDE systems contains the following arrays of Rosenbrock-Wanner method coefficients: ...
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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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### The Formula of Explicit Runge-Kutta Fourteen order

I need an explicit Runge-Kutta 14th order formula. If you know about some reference that discusses at least 10th order (or higher, since I'm looking for the 14th) of Runge-Kutta and there is ...
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### Solving differential equation in Python with discretized variable coefficients

I am trying to solve a differential equation with discretized variable coefficients which are calculated from a time serie. In this case the Runge-Kutta step size is fixed by the frequency in the time ...
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### Runge-Kutta in the presence of an attractor

Suppose you are solving a system of equations numerically that possesses an attractor (no matter the initial conditions set, all the different solutions will approach a specific set of values that ...
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### What exactly is the cause(s) of blow-up for too-large step size in a method like RK4?

I have been working on creating a few home-made numerical methods, and I am using them to visualize text-book problems from my Strogatz dynamics textbook. It feels like a good way to learn numerical ...
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