Questions tagged [accuracy]
For questions about characterizing or improving the accuracy of a computational method.
16
questions with no upvoted or accepted answers
9
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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 ...
- 1,320
5
votes
0
answers
686
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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 :)
...
- 128
5
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84
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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 ...
- 151
4
votes
0
answers
80
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Numerical algorithms made stable by unums which are unstable on IEEE floats
For unums, there is good evidence (see figure 5) that accuracy is better than IEEE floats. (Note: I use the term "unum" broadly to refer to any of the various iterations and revisions to the ...
- 2,085
3
votes
0
answers
152
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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 ...
- 2,085
3
votes
0
answers
118
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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
0
answers
230
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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 ...
- 435
3
votes
0
answers
180
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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 ...
- 131
2
votes
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answers
52
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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
0
answers
209
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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 ...
- 435
1
vote
0
answers
86
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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
0
answers
56
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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 = ...
- 321
0
votes
0
answers
21
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Oscillation in non-linear porous flow solved by finite difference
I am trying to solve numerically the flow of a gas through a porous, spherically symmetric body. The non-dimensional equations read:
$$
\frac{\partial\rho}{\partial t}+\tau\frac{1}{r^2}\frac{\partial}{...
0
votes
0
answers
37
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B-spline abscissa values for numerical stability
I am working with spline functions using the B-spline basis,
$$
f(x) = \sum_{i=1}^n c_i B_i(x;\mathbf{t})
$$
where the $B_i$ are cubic B-splines with a knot vector $\mathbf{t}$. For my application, ...
- 1,016
0
votes
0
answers
19
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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-...
- 2,085
0
votes
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51
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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 ...
- 301