Questions tagged [adaptive-timestepping]

The tag has no usage guidance.

2
votes
2answers
136 views

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 ...
2
votes
1answer
68 views

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 $c,b,\hat{b}$ ...
3
votes
1answer
103 views

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,...
2
votes
1answer
68 views

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 ...
2
votes
1answer
203 views

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 ...
1
vote
1answer
51 views

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 ...
3
votes
2answers
88 views

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 ...
0
votes
1answer
31 views

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 ...
0
votes
1answer
84 views

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 ...
3
votes
1answer
48 views

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. ...
2
votes
1answer
118 views

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 ...