Questions tagged [time-integration]
For questions about the particulars of solving differential equations with time as the independent variable.
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Time integration of first-order ODE with higher-order information
Suppose I wish to derive a numerical integrator for the first-order ODE $$x'(t)=F(x(t)).$$ By differentiating both sides of the expression in $t$, I can write a second-order relation also satisfied ...
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solve_ivp method=ODE23 time step not decreasing in order
My time step with the function scipy.integrate.solve_ivp is not decreasing in t_span fluctuating (reaching values below or ...
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Would a Co-simulation orchestrator work when a model uses a variable step size integrator
In every paper i was able to find, detailling the process of writing a co-simulation orchestrator (either Jacobi or Gauss-siedel), the paper assumed that both models were to compute their outputs on ...
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Synchronous integration vs asynchronous integration in simulations with complex problems
Lets say i want to create a detailed simulation of a complex system. For instance a drone.
This simulation will have to contain a few models, each one with it's own requirements, for instance
A 6Dof ...
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How to impose boundary conditions when solving a nonlinear dynamical system given by the FEM solver
I am solving a nonlinear dynamical system given by a nonlinear elastic problem which takes the following form:
$$ \boldsymbol{M} \ddot{u} + \boldsymbol{K}_{\textrm{NL}}u = 0 ,$$
here $u \in \mathbb{R}...
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mesh size restriction of spatial discretization in FEMs and FDMs
Is there any mesh size restriction of spatial discretization in FEMs and FDMs (finite difference)?
If a mesh is very coarse there is still perhaps nothing to stop the program from running and cause ...
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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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Does this second-order implicit Runge-Kutta method have a name?
I am studying the time-integration of the following paper,
Young, L. C. (1981). A finite-element method for reservoir simulation. Society of Petroleum Engineers Journal, 21(01), 115-128.
A copy (PDF)...
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How can I validate my time integration scheme for my dynamic linear elasticity FEM code with a manufactured solution or similar?
I am solving for a dynamic linear elasticity problem:
\begin{equation}
\dfrac{\partial^2 u}{\partial^2 t} - \nabla \cdot \sigma = f
\end{equation}
where $ u \in R^2 $ with sufficient BCs and ...
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Why do I get an oscillatory solution when applying the implicit trapezoidal method to the linear diffusion equation?
I wish to solve the following equation,
$$\frac{\partial f}{\partial t}=\frac{\partial}{\partial x}\left(D(x)\frac{\partial f}{\partial x}\right)$$
using an exponential integrator.
I discretize this ...
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Example: Velocity Verlet reduced accuracy
Velocity Verlet is often held to far more accurate than forward Euler while being no more expensive. Technically, this requires some degree of regularity on the potential. But, is there a convincing ...
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Need help to fully understand SciPy's odeint's reported step sizes, eval times, # of funct calls & total proc. time (re. question in Astronomy SE)
A recent question in Astronomy SE Numerical Programming using odeint takes more than 17 minutes got me interested in looking closer at SciPy's odeint.
The problem is a modified orbital mechanical ...
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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 ...
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Why is velocity Verlet better than Verlet for gravity if it has a worse order of magnitude for the error term
Even though this method is more widely used than the simple Verlet method mentioned above, it unfortunately has an error term of O(Δt^2)
, which is two orders of magnitude worse. That said, if you ...
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Numerov Method with Time Varying Potential
Is it possible to use the Numerov method to solve the Time Dependent Schrodinger Equation ($\frac{i\partial\Psi(x, y, z, t)}{\partial t} = \nabla^2\Psi(x, y, z, t) + \Psi(x, y, z, t)V(x, y, z, t)$) ...
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