Questions tagged [adaptive-timestepping]
The adaptive-timestepping tag has no usage guidance.
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Time step not converging in Transient simulation with RPI Wall boiling
I am trying to simulate subcooled flow boiling in horizontal channel with Non-equilibrium RPI wall boiling model. It is transient simulation with Implicit scheme. Steady state simulation are not ...
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ODE adaptive time stepping: is it bad to use "timescales of change" to select timestep size
Suppose you want to approximately solve a system of ODEs, using some numerical method (Euler, RK, BDF, whatever):
$\frac{du}{dt} = f(u)$
To do this you need to select time steps which solve the ODEs ...
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How to make a time-parametrization slower around a point but not too slow?
For animation purposes (see below) I need to use a parametrization which 'slows down' near a specific value;
More precisely, I am looking for a 'nice' monotonically increasing function $r:[0,1] \to [...
- 119
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How to select initial time step in adaptive time step ODE solver (TR-BDF2)
The Problem
I am currently reconstructing a TR-BDF2 scheme which contains the following two stages:
\begin{align}
y_{n+\gamma} & = y_n + \gamma \frac{h}{2}\left( f_n + f_{n+\gamma} \right) \...
- 152
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Adaptive Runge-Kutta for Stochastic (Projected) Gross-Pitaevskii Equation
I am using the XMDS library for solving the stochastic (projected) Gross-Pitaevskii equation
$$i \hbar \partial \Phi\left(\mathbf{r},t\right)_t=\hat{\mathcal{P}}\left\{(1-i \gamma)\left(\hat{H}_{\...
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Processing time steps in chunks with Fortran [closed]
My PDE simulation program written in Fortran has to make about 2 million variable time steps. But with each time step it slows down more and more, so that if it initially makes 1000 time steps per ...
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Implementing adaptive timestepping in CUDA
I want to implement a CUDA solver for the 2D shallow water equations using adaptive timestepping with a Courant number fixed by the user. The algorithm pseudocode looks something like this:
...
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Automatic timestep adjustment in a CFD solver
I have developed my own 3D Finite Volume Navier-Stokes solver based on projection method for nonuniform grid. I am looking to incorporate automatic timestep adjustment at each time step based on ...
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Dormand–Prince 5(4): How to update the stepsize and make accept/reject decision?
https://en.wikipedia.org/wiki/Dormand–Prince_method
I want to implement the Dormand-Prince 4(5) version to solve Initial Value problems. Using regular notation I have $A$ matrix and the $c,b,\hat{b}$ ...
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Time integration of wave equation
My question is: how come that certain formulations of the wave equation can be time integrated more efficiently then others?
Le me expand a bit on that. Consider the wave equation:
$$ \frac{d^2 p(t,...
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Step size updating scheme adaptive embedded RK methods
If I have a RK method $y$ of order $p$ and a RK method $z$ of order $p-1$ I have read I can estimate the local error as $r_{n+1} = y_{n+1} - z_{n+1}$. First of all I don't see how this estimates the ...
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Step-size selection for an Trapezoidal Method ODE solver (ode23t)
I was reading the documentation of the MatLab ODE solver ode23t, and I've seen that the trapezoidal rule is used.
Moreover, the error is estimated by ...
- 540
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Wanted: smoothing time domain transform
Let $A$ be a finite (and small-ish) set of positive real numbers and 0. Let $B$ be a subset of $\mathbb N^0$, up to some (small-ish) bound.
I have a function $f(t)$, $A \rightarrow B$ that is ...
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Error control and sequence acceleration at the same time
In a posteriori error control for solving ODEs, one typically computes two different approximate solutions, one of which being "more accurate" and one of which being "less accurate". If $y_q^{n+1}$ is ...
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Confirmation of FSAL property for IMEX methods by Kennedy and Carpenter
This question is a continuation of
Fourth order IMEX Runge-Kutta method and Implementation details for high order IMEX methods by Kennedy and Carpenter.
I need confirmation that ARK3(2)4L[2]SA by ...
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Is the time step size of a Rosenbrock method for stiff systems iteratively calculated?
I have an ODE system of the general form
y' = k(y)(x) + q(z)(x)
x' = a(z)(x) + b(x)(x)
where k,q,a and b are also dependent on the states x and y. The ...
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Testing Wiener process splitting in adaptive-step SDE integrators
I am investigating various methods for adaptive-step integration of stochastic differential equations and trying to implement them. All of the papers that I've seen (e.g. H. Lamba, J. Comp. App. Math. ...
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Open source solver for continuous-time stochastic non-linear DAEs (SDAEs)
I am trying to solve a system of non-linear index-1 DAEs in which the derivatives of the state variables, $x(t)$ are corrupted by additive noise, $w(t)$ (whose covariance matrix is known).
$\dot x(t) =...
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Adaptive Timestepping for Stong Stability Preserving (SSP) Runge-Kutta Methods
Are there error estimators and research on adaptive timestepping schemes for SSPRK methods? My Googling could not uncover papers which addressed this, so I was wondering if there was anything ...
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How do you numerically solve a multivariable ODE system with different time steps per state variable?
If you have a large multivariable ODE system, and certain processes occur at a much shorter time scale, how can you implement a solver that uses smaller time steps for state variables involved in fast ...
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