The time-integration tag has no wiki summary.
1
vote
0answers
39 views
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} ...
4
votes
2answers
80 views
Improving the time integration of implicit discretized PDE with a non-linear source term
This might be a naive question, but when applying a implicit discretization to a PDE with a source term, should the source be averaged in time? For example if we take the diffusion equation with a ...
4
votes
1answer
53 views
Energy Conservation
I'm working on a time integration scheme for my research. As a result, I have come across an interesting phenomenon. Somehow, the total energy of the scheme oscillates. At any given time the total ...
9
votes
2answers
153 views
What is pseudo time-stepping?
While reading some literature on PDE solvers I came across the term pseudo time-stepping today. It seems to be a common term, however I failed to find a good definition or an introductionary article ...
12
votes
1answer
159 views
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 ...
2
votes
2answers
102 views
What are good examples of problems which are stiff due to very long interval of integration?
There is a class of stiff initial value problems for ODEs that have small Lipschitz constants, slowly-changing solutions, but very long interval of integration. The only practical example of such a ...
0
votes
0answers
62 views
How to solve the following differential equations using ode functions of Matlab_part2? [closed]
This post is the ccontinuation of this pose enter link description here
...
0
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0answers
83 views
How to solve the following differential equations using ode functions of Matlab_part1? [closed]
As shown in the following matlab program which is used to find numerical solutions of a dynamic equations (differential equations) which are developed by Lagrange method, the ...
6
votes
1answer
68 views
Linearized implicit time stepping
Consider the general FD implicit time stepping scheme
$\frac{x_{t+1} - x_t}{\Delta t} = f(x_{t+1})$,
where $x$ is the vector variable of interest and $f$ is some function, generally non-linear.
...
7
votes
1answer
96 views
Demonstrating that the time step size is small enough in a code with automatic step size selection
I recently inherited a large body of legacy code that solves a very stiff, transient problem. I would like to demonstrate that the spatial and temporal step sizes are small enough that the ...
10
votes
5answers
250 views
Examples of PDE computations using parallelism in both space and time
In the numerical solution of initial boundary value PDEs, it is very common to employ parallelism in space. It is much less common to employ some form of parallelism in the time discretization, and ...
6
votes
1answer
59 views
How do you change the desired accuracy of a TS object in PETSc?
I'm currently getting very long propagation times when attempting to use the Time Stepping propagators in Petsc 3.2, and in the interest of speeding things up, I'm curious how I can reduce the ...
8
votes
3answers
305 views
Can I use an explicit time stepping scheme to determine numerically whether an ODE is stiff?
I have an ODE:
$u'=-1000u+sin(t)$
$u(0)=-\frac{1}{1000001}$
I know that this particular ODE is stiff, analytically. I also know that if we use an explicit (forward) time stepping method ...
