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Questions tagged [runge-kutta-methods]

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

Topics in this tag include:

  • The standard 4-stage Runge–Kutta method.
  • Other iterative numerical methods that belong to the family of Runge–Kutta methods.
  • The application of Runge–Kutta method in providing numerical solutions to mathematical models.

When posting in this tag, consider attaching these more general tags below, if they are applicable:

464 questions
2
votes
2 answers

Is is possible to use Runge-Kutta RK4 on the three body problem?

I have just learned about the RK4 method for approximating differential equations. Is it possible for this to be applied to the three-body problem?
MathStud912
  • 91
2
votes
1 answer

Runge-Kutta method for higher-order differential equations

I am studying Numerical Analysis with the book of Richard L.Burden. A question which I'm struggling with right now is following. Transform the second-order initial-value problem $y'' - 2y' + 2y = e^{2t}\sin t$ for $0 \leq t \leq 1, $ with $y(0) =…
James
  • 23
1
vote
0 answers

Runge-Kutta method for state space with input

I need to implement the 4th order Runge-Kutta method to propagate an affine non linear system. My doubt is in regards on how the input should be treated when calculating the k parameters. To be more specific, consider the affine non linear system…
Darren DeBattista
  • 163
1
vote
1 answer

deriving an implicit Runge Kutta method from its Butcher tableau

I would like to use the Gauss–Legendre method of order four (which is a particular Runge Kutta method) to solve numerically an ode but I find only it's Butcher Tableau and I fail to derive the method . You can find the Tableau here…
nathan raynal
  • 253
0
votes
1 answer

Systematic approximation to derivative of Runge-Kutta integral with respect to a parameter?

Suppose I have a differential equation $\frac{d}{dt}y(t,\lambda) = f(y(t,\lambda),\lambda)$ where $\lambda$ is some parameter of the system. The initial value $y(0,\lambda)$ is specified. I am looking for a good way to estimate…
Ian Holmes
  • 1
0
votes
0 answers

Coefficient, constant or parameter of Runge-Kutta Method?

I confused are $a_i$, $b_i$ and $c_i$ Coefficient, constant or parameter of Runge-Kutta Method? see https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods Because there is mention it coefficient, constant and parameter on different site. Thank…
konyong
  • 85
0
votes
1 answer

Show solution from Runge Kutta program is correct to 5 decimal places

I have built a program which implements RK4 method to solve ODEs. I want to show my program can find a specific value correct to 5 decimal places. How would I prove this?
user3376601
  • 105
  • 3
0
votes
1 answer

Acquiring a function from a butcher table? (Runge-Kutta)

When I have this butcher table: \begin{array} {c|cccc} 0\\ c & c\\ \hline & (1-d) &d \end{array} I got this equation: $\phi(x,y,h) = (1-d)*f(x,y) + d*f(x+ch, y+ch*f(x,y))$ Now I need to know the $\phi(x,y,h)$ function for this…
user648748
0
votes
0 answers

Simplifying Runge-Kutta Fourth Order (with redneck math)

Please note I am no mathematician, and this has been a struggle for me to understand the concepts below. I have several questions regarding the Runge-Kutta 4th order formula. "deltaTime" is my overall fixed time step. (Q1) How to perform the math…
Nicholas
  • 29