Computational Science Stack Exchange
Computational Science Stack Exchange

Questions tagged [time-integration]

For questions about the particulars of solving differential equations with time as the independent variable.

167 questions
15
votes
1 answer

What is the correct way of integrating in astronomy simulations?

I'm creating a simple astronomy simulator that should use Newtonian physics to simulate movement of planets in a system (or any objects, for that matter). All the bodies are circles in an Euclidean plane, that have properties such as position,…
jcora
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14
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4 answers

Why are Runge-Kutta and Euler's method so different?

I am solving a system of linear equations, $\underline {\dot x}=\underline A\cdot \underline x$, numerically. I have done this using the popular of methods of Euler and Runge-Kutta (RK). I have noticed quite a difference between the two in accuracy…
user16937
6
votes
4 answers

Numerical integration of non-uniform acceleration samples

I'm given a stream of acceleration data with timestamps. The sampling is non-uniform. Apart from Euler, is there a way to integrate the acceleration into velocity? Something more accurate or of higher order? I can store some past acceleration data,…
user1071136
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4
votes
1 answer

Behavior of integration method

I was playing with N-body simulations of a game called Kerbal Space Program, which itself uses the patched conics approximation. I have read that for long term stability it is best to use symplectic integrators and one of the simplest would be…
fibonatic
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2
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Strong stability preserving RK scheme

For the ODE $$ \dot{x} = f(x) $$ we have the 2-stage, second order SSP RK scheme (Shu, Osher, Gottlieb) $$ x^{(0)} = x^n $$ $$ x^{(1)} = x^{(0)} + \Delta t f(x^{(0)}) $$ $$ x^{(2)} = \frac{1}{2} x^n + \frac{1}{2}[ x^{(1)} + \Delta t…
cfdlab
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2
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1 answer

Time integrator for a WENO scheme for advection equation

I'm implementing a finite-difference WENO scheme for a simple advection equation $$ \frac{\partial u}{\partial t} + \frac{\partial u}{\partial x} = 0 $$ with periodic boundary conditions. I'm not quite sure my scheme is conventional since it is…
uranix
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2
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1 answer

Numerical integration of a function whose expression is unknown

I want to compute the value of an integral of a function. This function, however, is not given by a formula, say $f(x) \: \forall x \in [0,1]$, but is only known through its values on some given points, say $f \left(\frac{k}{n} \right) \: \forall k…
bela83
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1
vote
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Velocity Verlet leading to faster simulation than Euler in an n-Body simulation?

I have all the constants set to the same values for each set of code, G, the timestep, the masses of the planets etc. But using Velocity Verlet doesn't work unless I lower the gravitational constant because otherwise the gravitational pull is too…
ght007
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