# Questions tagged [runge-kutta-methods]

For questions about the family of Runge–Kutta methods and their application in numerical methods.

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### Global truncation error of backward Euler method

It's often found in books that the global truncation error of the forward Euler method applied to $\dot{y} (t) = f(t, y(t))$ is given by something like $$\frac{\exp(LT) -1}{L} \frac{Mh}{2},$$ with $L$...
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### Runge Kutta Method for in $1+1$ dimension

Given a partial differential equation $\partial_t u(t,x) = F(t,x,u,u')$ Suppose I know the functions $u(t_0,x)$ and $u'(t_0,x)$ at some point $t_0$ for all $x$. In order to obtain the function $u$ at ...
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### How is the E coefficients calculated or generated for the Radau IIA 5th Order?

With regard to Scipy, the E coefficients are written out. I've seen this from different sources as well. However, I cannot find any reference to how the E coefficients were computed.
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### Explicit Runge-Kutta method for solving ODE

I would like to understand in some detail why this Runge-Kutta method is explicit if and only if $c_1=0$. Why in this case the r.h.s. doesn't contain $y_{n+1}$ ? EDIT $c_1=0$ EDIT 2 I would also like ...
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### How to solve this autonomous DE with RK 4?

I have this equation : $$\frac{d\alpha}{dz} = - \frac{dr}{dz} * \frac{\tan(\alpha)}r$$ I searched for some similar examples but non of these equations was like this one. I'm confused about this one. ...
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### An adaptive step size solver for an ODE

I am trying solve an ordinary differential equation numerically, $\,dy/dt=10e^{-(t-2)^2/2(0.075)^2}-0.6y\,\,$ with an initial value and initial step size between $t=0\, and\, t=4$. In my code I ...
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