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Results tagged with implicit-methods
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Implicit methods are timestepping methods that use an inversion at every timestep. This allows for much better stability properties than explicit methods, though it comes with a serious speed penalty in some cases. Examples of implicit methods include Backward Euler and Crank-Nicholson.
1
vote
Fluent time step size (transient implicit solver)
You've given scant details for your problem, so I can only quote general trends.
Time step size affects numerical error and stability. If you pick a really large step size, your results may be meanin …
- 30.4k
1
vote
Accepted
Implicit ODE solver with discontinuous derivatives
With the discussion clearing up some of the confusion in the original post, here is a summary of the discussion so far:
I want to implement an implicit ODE solver, but don't know what to do when t …
- 30.4k
155
votes
Accepted
Recommendations for a usable, fast C++ matrix library?
I've gathered the following from online research so far:
I've used Armadillo a little bit, and found the interface to be intuitive enough, and it was easy to locate binary packages for Ubuntu (and I' …
2
votes
Not getting correct numerical solution for Advection-Diffusion-Reaction eqn
One of the best ways to test a PDE solver is to use the method of manufactured solutions. Essentially, you modify the PDE (and discretization) by adding a source term that yields an exact solution kno …
- 30.4k
2
votes
Accepted
Matlab solution for implicit finite difference heat equation with kinetic reactions
It looks like the model you're trying to solve is:
\begin{align}
(1/\alpha(w,c))T_{t}(r,t) &= T_{rr}(r,t) + (p/r) \cdot T_{r}(r,t) \\
w_{t}(r,t) &= -(k_{1}(T(r,t)) + k_{2}(T(r,t)) + k_{3}(T(r,t)))w(r …
- 30.4k
2
votes
Accepted
Implicit heat diffusion with kinetic reactions
As I said in my answer to your previous question, it's probably better if you don't try to write your own ODE solver, which is what you are doing now. There are a lot of good libraries out there that …
- 30.4k
2
votes
How to add reaction and source terms to a diffusion PDE solver written with MATLAB's pdepe f...
Since pdepe accepts systems of PDEs through vector-valued capacity, flux, and source terms, one way to accommodate your request would be to set the fluxes for all of the $\rho$ variables equal to zero …
- 30.4k