Questions tagged [adaptive-timestepping]

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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 ...
Liril Silvi's user avatar
1 vote
2 answers

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 ...
nicholaswogan's user avatar
1 vote
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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 [...
Asaf Shachar's user avatar
2 votes
1 answer

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) \...
kostas1335's user avatar
2 votes
1 answer

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}_{\...
Jack G's user avatar
  • 21
2 votes
0 answers

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 ...
sequence's user avatar
  • 216
1 vote
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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: ...
hertzsprung's user avatar
2 votes
2 answers

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 ...
mechieCoder's user avatar
2 votes
1 answer

Dormand–Prince 5(4): How to update the stepsize and make accept/reject decision?–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 $c,b,\hat{b}$ ...
k.dkhk's user avatar
  • 255
3 votes
1 answer

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,...
user21's user avatar
  • 382
2 votes
1 answer

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 ...
Heuristics's user avatar
2 votes
1 answer

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 ...
VoB's user avatar
  • 540
1 vote
1 answer

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 ...
rsp1984's user avatar
  • 435
3 votes
2 answers

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 ...
A. B. Marnie's user avatar
0 votes
1 answer

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 ...
Raibyo's user avatar
  • 219
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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 ...
Nirjhar Alam's user avatar
3 votes
1 answer

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. ...
fjarri's user avatar
  • 133
1 vote
1 answer

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) =...
Dr Krishnakumar Gopalakrishnan's user avatar
2 votes
1 answer

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 ...
Chris Rackauckas's user avatar
8 votes
2 answers

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 ...
bmillare's user avatar
  • 181