Questions tagged [accuracy]
The accuracy tag has no usage guidance.
13
questions with no upvoted or accepted answers
9
votes
0answers
437 views
Updating matrix diagonal with Woodbury matrix identity and maintaining numerical accuracy
I have a dense matrix A and its corresponding inverse $A^{-1}$. The Woodbury matrix identity states:
$$ (A + UCV)^{-1} = A^{-1} - A^{-1}U(C^{-1} + VA^{-1}U)^{-1}VA^{-1} $$
I wish to perform small ...
5
votes
0answers
536 views
Order of accuracy of FVM discretization
I've recently got interested in CFD and started a small project by solving the radial Reynoldsequation. Why the Reynoldsequation? I recently encountered it through my studies and somehow got stuck :)
...
5
votes
0answers
79 views
Order of convergence of Scrodinger eq. with CN scheme
I'm trying to solve numerically the 1-dim time dependent Schrodinger equation using the Crank Nicolson scheme and the Thomas algorithm to solve the tridiagonal matrix.
The physical system consists of ...
3
votes
0answers
140 views
Derivative of Whittaker-Shannon interpolant
Last time we looked at how to improve the accuracy of Whittaker-Shannon interpolation, where user njuffa demonstrated that judicious use of sin_pi could greatly ...
3
votes
0answers
107 views
How can I evaluate the accuracy of my n-body simulation?
I am making an n-body simulation in python. There are many different methods to numerically solve the system of differential equations governing the gravitational interactions between the $n$ ...
3
votes
0answers
212 views
Computing accuracy of my finite difference scheme for uniform grid on a non-uniform grid
I have a ADI finite difference scheme for the 2D Navier-Stokes equations that uses a second order accurate (central) approximation for the advective terms. I am ignoring the diffusive terms for now. I ...
3
votes
0answers
173 views
How to accurately decompose positive semidefinite matrix and use the lower triangular part in linear equations
I have $n$ arbitrary $p\times 1$ vectors $x_i$, and $p\times k$ matrices $A_i$, and $n$ $p \times p$ positive semidefinite matrices $S_i$, where some (often most) of the $S_i$'s are same (for example ...
2
votes
0answers
49 views
Quick evaluation of floating point Absolute Error
I need to to find a quick and dirty way to estimate the absolute error introduced by a series of agebraic operations of IEEE single precision floating point numbers, a pessimistic result is ok.
The ...
2
votes
0answers
183 views
boundary conditions with non-constant coefficients in cell centred finite volume method
Suppose am solving the heat conduction equation in 1d with
Dirichlet boundary conditions. The thermal conductivity $k$ is a non
constant function.
So $-(k(x)u'(x))' = f(x)$
The value of $k$ enters the ...
1
vote
0answers
45 views
Comparison between stability and accuracy of various Finite Difference schemes
I`m Analyzing the 1D convection equation (PDE) for stability, consistency, and accuracy.
I know Both upwind schemes (explicit and implicit) show better stability with a higher number of waves for ...
1
vote
0answers
52 views
Decrease in slope during convergence analysis
I am using the method of manufactured solutions to perform the order of accuracy testing. I am using a cube for the testing. The cube is size 1m on all sides.
I used 5 refinements:
$dx = dy = dz = ...
0
votes
0answers
18 views
Cost functions to judge time/memory/accuracy tradeoffs
I am working on an interesting algorithm: Its absolute error is exponential in a parameter $j \in \mathbb{N}$, and for a given $j$, I have complete freedom to choose between an $\mathcal{O}(1)$ time-...
0
votes
0answers
47 views
Order of accuracy of linearised vs non-linear system
Does the order of accuracy of a combination of schemes applied to solve a system of non-linear equations, match those of the same schemes applied to the linearised version of the system?
In other ...
